{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0001","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-12]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(1, 1)","explanation_zh":"尺寸=(1, 1)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071001,"parameters":{"M":[[-12]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[1,1],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0002","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-11, -12]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(1, 2)","explanation_zh":"尺寸=(1, 2)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071002,"parameters":{"M":[[-11,-12]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[1,2],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0003","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-10, -11, -12]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(1, 3)","explanation_zh":"尺寸=(1, 3)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071003,"parameters":{"M":[[-10,-11,-12]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[1,3],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0004","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-9, -10, -11, -12]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(1, 4)","explanation_zh":"尺寸=(1, 4)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071004,"parameters":{"M":[[-9,-10,-11,-12]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[1,4],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0005","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-8, -9, -10, -11, -12]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(1, 5)","explanation_zh":"尺寸=(1, 5)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071005,"parameters":{"M":[[-8,-9,-10,-11,-12]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[1,5],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0006","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-7], [-5]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(2, 1)","explanation_zh":"尺寸=(2, 1)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071006,"parameters":{"M":[[-7],[-5]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[2,1],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0007","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-6, -7], [-4, -5]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(2, 2)","explanation_zh":"尺寸=(2, 2)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071007,"parameters":{"M":[[-6,-7],[-4,-5]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[2,2],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0008","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-5, -6, -7], [-3, -4, -5]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(2, 3)","explanation_zh":"尺寸=(2, 3)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071008,"parameters":{"M":[[-5,-6,-7],[-3,-4,-5]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[2,3],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0009","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-4, -5, -6, -7], [-2, -3, -4, -5]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(2, 4)","explanation_zh":"尺寸=(2, 4)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071009,"parameters":{"M":[[-4,-5,-6,-7],[-2,-3,-4,-5]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[2,4],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0010","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-3, -4, -5, -6, -7], [-1, -2, -3, -4, -5]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(2, 5)","explanation_zh":"尺寸=(2, 5)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071010,"parameters":{"M":[[-3,-4,-5,-6,-7],[-1,-2,-3,-4,-5]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[2,5],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0011","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-2], [0], [2]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(3, 1)","explanation_zh":"尺寸=(3, 1)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071011,"parameters":{"M":[[-2],[0],[2]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[3,1],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0012","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-1, -2], [1, 0], [3, 2]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(3, 2)","explanation_zh":"尺寸=(3, 2)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071012,"parameters":{"M":[[-1,-2],[1,0],[3,2]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[3,2],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0013","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[0, -1, -2], [2, 1, 0], [4, 3, 2]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(3, 3)","explanation_zh":"尺寸=(3, 3)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071013,"parameters":{"M":[[0,-1,-2],[2,1,0],[4,3,2]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[3,3],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0014","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[1, 0, -1, -2], [3, 2, 1, 0], [5, 4, 3, 2]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(3, 4)","explanation_zh":"尺寸=(3, 4)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071014,"parameters":{"M":[[1,0,-1,-2],[3,2,1,0],[5,4,3,2]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[3,4],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0015","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[2, 1, 0, -1, -2], [4, 3, 2, 1, 0], [6, 5, 4, 3, 2]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(3, 5)","explanation_zh":"尺寸=(3, 5)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071015,"parameters":{"M":[[2,1,0,-1,-2],[4,3,2,1,0],[6,5,4,3,2]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[3,5],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0016","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[3], [5], [7], [9]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(4, 1)","explanation_zh":"尺寸=(4, 1)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071016,"parameters":{"M":[[3],[5],[7],[9]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[4,1],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0017","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[4, 3], [6, 5], [8, 7], [10, 9]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(4, 2)","explanation_zh":"尺寸=(4, 2)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071017,"parameters":{"M":[[4,3],[6,5],[8,7],[10,9]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[4,2],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0018","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[5, 4, 3], [7, 6, 5], [9, 8, 7], [11, 10, 9]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(4, 3)","explanation_zh":"尺寸=(4, 3)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071018,"parameters":{"M":[[5,4,3],[7,6,5],[9,8,7],[11,10,9]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[4,3],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0019","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[6, 5, 4, 3], [8, 7, 6, 5], [10, 9, 8, 7], [12, 11, 10, 9]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(4, 4)","explanation_zh":"尺寸=(4, 4)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071019,"parameters":{"M":[[6,5,4,3],[8,7,6,5],[10,9,8,7],[12,11,10,9]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[4,4],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0020","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(4, 5)","explanation_zh":"尺寸=(4, 5)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071020,"parameters":{"M":[[7,6,5,4,3],[9,8,7,6,5],[11,10,9,8,7],[13,12,11,10,9]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[4,5],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0021","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[8], [10], [12], [14], [16]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(5, 1)","explanation_zh":"尺寸=(5, 1)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071021,"parameters":{"M":[[8],[10],[12],[14],[16]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[5,1],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0022","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[9, 8], [11, 10], [13, 12], [15, 14], [17, 16]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(5, 2)","explanation_zh":"尺寸=(5, 2)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071022,"parameters":{"M":[[9,8],[11,10],[13,12],[15,14],[17,16]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[5,2],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0023","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[10, 9, 8], [12, 11, 10], [14, 13, 12], [16, 15, 14], [18, 17, 16]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(5, 3)","explanation_zh":"尺寸=(5, 3)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071023,"parameters":{"M":[[10,9,8],[12,11,10],[14,13,12],[16,15,14],[18,17,16]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[5,3],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0024","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[11, 10, 9, 8], [13, 12, 11, 10], [15, 14, 13, 12], [17, 16, 15, 14], [19, 18, 17, 16]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(5, 4)","explanation_zh":"尺寸=(5, 4)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071024,"parameters":{"M":[[11,10,9,8],[13,12,11,10],[15,14,13,12],[17,16,15,14],[19,18,17,16]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[5,4],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0025","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"非空矩陣尺寸","stem_zh":"實矩陣，橫列／直行次序固定，M=[[12, 11, 10, 9, 8], [14, 13, 12, 11, 10], [16, 15, 14, 13, 12], [18, 17, 16, 15, 14], [20, 19, 18, 17, 16]]。求 (橫列數, 直行數)，每邊為1至5。","answer":{"kind":"short_text","value":"(5, 5)","explanation_zh":"尺寸=(5, 5)。先驗矩形等長橫列，再計兩個維度，不把元素個數當其中一個邊長。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["非空矩陣尺寸"]},"variant":{"family_id":"qf-matrix-shape","seed":202610071025,"parameters":{"M":[[12,11,10,9,8],[14,13,12,11,10],[16,15,14,13,12],[18,17,16,15,14],[20,19,18,17,16]],"operation":"matrix_shape","domain":"reals","semantic_template":"qf-matrix-shape/{\"inputs\":[5,5],\"operation\":\"matrix_shape\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0026","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-12]]。索引由1起算，求第 1 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"-12","explanation_zh":"M(1,1)=-12。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071026,"parameters":{"M":[[-12]],"i":1,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[1,1,1,1,\"-12\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0027","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-11, -12]]。索引由1起算，求第 1 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"-11","explanation_zh":"M(1,1)=-11。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071027,"parameters":{"M":[[-11,-12]],"i":1,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[1,2,1,1,\"-11\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0028","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-10, -11, -12]]。索引由1起算，求第 1 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"-10","explanation_zh":"M(1,1)=-10。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071028,"parameters":{"M":[[-10,-11,-12]],"i":1,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[1,3,1,1,\"-10\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0029","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-9, -10, -11, -12]]。索引由1起算，求第 1 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"-9","explanation_zh":"M(1,1)=-9。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071029,"parameters":{"M":[[-9,-10,-11,-12]],"i":1,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[1,4,1,1,\"-9\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0030","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-8, -9, -10, -11, -12]]。索引由1起算，求第 1 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"-8","explanation_zh":"M(1,1)=-8。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071030,"parameters":{"M":[[-8,-9,-10,-11,-12]],"i":1,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[1,5,1,1,\"-8\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0031","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-7], [-5]]。索引由1起算，求第 2 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"-5","explanation_zh":"M(2,1)=-5。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071031,"parameters":{"M":[[-7],[-5]],"i":2,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[2,1,2,1,\"-5\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0032","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-6, -7], [-4, -5]]。索引由1起算，求第 1 橫列、第 2 直行元素。","answer":{"kind":"short_text","value":"-7","explanation_zh":"M(1,2)=-7。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071032,"parameters":{"M":[[-6,-7],[-4,-5]],"i":1,"j":2,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[2,2,1,2,\"-7\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0033","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-5, -6, -7], [-3, -4, -5]]。索引由1起算，求第 2 橫列、第 2 直行元素。","answer":{"kind":"short_text","value":"-4","explanation_zh":"M(2,2)=-4。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071033,"parameters":{"M":[[-5,-6,-7],[-3,-4,-5]],"i":2,"j":2,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[2,3,2,2,\"-4\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0034","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-4, -5, -6, -7], [-2, -3, -4, -5]]。索引由1起算，求第 1 橫列、第 2 直行元素。","answer":{"kind":"short_text","value":"-5","explanation_zh":"M(1,2)=-5。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071034,"parameters":{"M":[[-4,-5,-6,-7],[-2,-3,-4,-5]],"i":1,"j":2,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[2,4,1,2,\"-5\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0035","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-3, -4, -5, -6, -7], [-1, -2, -3, -4, -5]]。索引由1起算，求第 2 橫列、第 2 直行元素。","answer":{"kind":"short_text","value":"-2","explanation_zh":"M(2,2)=-2。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071035,"parameters":{"M":[[-3,-4,-5,-6,-7],[-1,-2,-3,-4,-5]],"i":2,"j":2,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[2,5,2,2,\"-2\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0036","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-2], [0], [2]]。索引由1起算，求第 2 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"0","explanation_zh":"M(2,1)=0。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071036,"parameters":{"M":[[-2],[0],[2]],"i":2,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[3,1,2,1,\"0\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0037","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-1, -2], [1, 0], [3, 2]]。索引由1起算，求第 3 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"3","explanation_zh":"M(3,1)=3。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071037,"parameters":{"M":[[-1,-2],[1,0],[3,2]],"i":3,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[3,2,3,1,\"3\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0038","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[0, -1, -2], [2, 1, 0], [4, 3, 2]]。索引由1起算，求第 1 橫列、第 3 直行元素。","answer":{"kind":"short_text","value":"-2","explanation_zh":"M(1,3)=-2。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071038,"parameters":{"M":[[0,-1,-2],[2,1,0],[4,3,2]],"i":1,"j":3,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[3,3,1,3,\"-2\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0039","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[1, 0, -1, -2], [3, 2, 1, 0], [5, 4, 3, 2]]。索引由1起算，求第 2 橫列、第 3 直行元素。","answer":{"kind":"short_text","value":"1","explanation_zh":"M(2,3)=1。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071039,"parameters":{"M":[[1,0,-1,-2],[3,2,1,0],[5,4,3,2]],"i":2,"j":3,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[3,4,2,3,\"1\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0040","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[2, 1, 0, -1, -2], [4, 3, 2, 1, 0], [6, 5, 4, 3, 2]]。索引由1起算，求第 3 橫列、第 3 直行元素。","answer":{"kind":"short_text","value":"4","explanation_zh":"M(3,3)=4。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071040,"parameters":{"M":[[2,1,0,-1,-2],[4,3,2,1,0],[6,5,4,3,2]],"i":3,"j":3,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[3,5,3,3,\"4\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0041","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[3], [5], [7], [9]]。索引由1起算，求第 4 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"9","explanation_zh":"M(4,1)=9。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071041,"parameters":{"M":[[3],[5],[7],[9]],"i":4,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[4,1,4,1,\"9\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0042","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[4, 3], [6, 5], [8, 7], [10, 9]]。索引由1起算，求第 1 橫列、第 2 直行元素。","answer":{"kind":"short_text","value":"3","explanation_zh":"M(1,2)=3。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071042,"parameters":{"M":[[4,3],[6,5],[8,7],[10,9]],"i":1,"j":2,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[4,2,1,2,\"3\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0043","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[5, 4, 3], [7, 6, 5], [9, 8, 7], [11, 10, 9]]。索引由1起算，求第 2 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"7","explanation_zh":"M(2,1)=7。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071043,"parameters":{"M":[[5,4,3],[7,6,5],[9,8,7],[11,10,9]],"i":2,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[4,3,2,1,\"7\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0044","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[6, 5, 4, 3], [8, 7, 6, 5], [10, 9, 8, 7], [12, 11, 10, 9]]。索引由1起算，求第 3 橫列、第 4 直行元素。","answer":{"kind":"short_text","value":"7","explanation_zh":"M(3,4)=7。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071044,"parameters":{"M":[[6,5,4,3],[8,7,6,5],[10,9,8,7],[12,11,10,9]],"i":3,"j":4,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[4,4,3,4,\"7\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0045","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]]。索引由1起算，求第 4 橫列、第 4 直行元素。","answer":{"kind":"short_text","value":"10","explanation_zh":"M(4,4)=10。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071045,"parameters":{"M":[[7,6,5,4,3],[9,8,7,6,5],[11,10,9,8,7],[13,12,11,10,9]],"i":4,"j":4,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[4,5,4,4,\"10\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0046","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[8], [10], [12], [14], [16]]。索引由1起算，求第 1 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"8","explanation_zh":"M(1,1)=8。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071046,"parameters":{"M":[[8],[10],[12],[14],[16]],"i":1,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[5,1,1,1,\"8\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0047","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[9, 8], [11, 10], [13, 12], [15, 14], [17, 16]]。索引由1起算，求第 2 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"11","explanation_zh":"M(2,1)=11。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071047,"parameters":{"M":[[9,8],[11,10],[13,12],[15,14],[17,16]],"i":2,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[5,2,2,1,\"11\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0048","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[10, 9, 8], [12, 11, 10], [14, 13, 12], [16, 15, 14], [18, 17, 16]]。索引由1起算，求第 3 橫列、第 2 直行元素。","answer":{"kind":"short_text","value":"13","explanation_zh":"M(3,2)=13。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071048,"parameters":{"M":[[10,9,8],[12,11,10],[14,13,12],[16,15,14],[18,17,16]],"i":3,"j":2,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[5,3,3,2,\"13\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0049","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[11, 10, 9, 8], [13, 12, 11, 10], [15, 14, 13, 12], [17, 16, 15, 14], [19, 18, 17, 16]]。索引由1起算，求第 4 橫列、第 1 直行元素。","answer":{"kind":"short_text","value":"17","explanation_zh":"M(4,1)=17。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071049,"parameters":{"M":[[11,10,9,8],[13,12,11,10],[15,14,13,12],[17,16,15,14],[19,18,17,16]],"i":4,"j":1,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[5,4,4,1,\"17\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0050","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"由1起算的指定矩陣元素","stem_zh":"實矩陣，橫列／直行次序固定，M=[[12, 11, 10, 9, 8], [14, 13, 12, 11, 10], [16, 15, 14, 13, 12], [18, 17, 16, 15, 14], [20, 19, 18, 17, 16]]。索引由1起算，求第 5 橫列、第 5 直行元素。","answer":{"kind":"short_text","value":"16","explanation_zh":"M(5,5)=16。索引須在明示維度內；其他位置的元素不改變此讀值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["由1起算的指定矩陣元素"]},"variant":{"family_id":"qf-matrix-entry","seed":202610071050,"parameters":{"M":[[12,11,10,9,8],[14,13,12,11,10],[16,15,14,13,12],[18,17,16,15,14],[20,19,18,17,16]],"i":5,"j":5,"operation":"matrix_entry","domain":"reals","semantic_template":"qf-matrix-entry/{\"inputs\":[5,5,5,5,\"16\"],\"operation\":\"matrix_entry\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0051","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-12]]、B=[[12]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0]]","explanation_zh":"和矩陣=[[0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071051,"parameters":{"A":[[-12]],"B":[[12]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-12\"]],[[\"12\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0052","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-11, -12]]、B=[[2, 4]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8]]","explanation_zh":"和矩陣=[[-9, -8]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071052,"parameters":{"A":[[-11,-12]],"B":[[2,4]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-11\",\"-12\"]],[[\"2\",\"4\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0053","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-10, -11, -12]]、B=[[1, 3, 5]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7]]","explanation_zh":"和矩陣=[[-9, -8, -7]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071053,"parameters":{"A":[[-10,-11,-12]],"B":[[1,3,5]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-10\",\"-11\",\"-12\"]],[[\"1\",\"3\",\"5\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0054","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-9, -10, -11, -12]]、B=[[9, 10, 11, 12]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0, 0, 0, 0]]","explanation_zh":"和矩陣=[[0, 0, 0, 0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071054,"parameters":{"A":[[-9,-10,-11,-12]],"B":[[9,10,11,12]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-9\",\"-10\",\"-11\",\"-12\"]],[[\"9\",\"10\",\"11\",\"12\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0055","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-8, -9, -10, -11, -12]]、B=[[-1, 1, 3, 5, 7]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7, -6, -5]]","explanation_zh":"和矩陣=[[-9, -8, -7, -6, -5]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071055,"parameters":{"A":[[-8,-9,-10,-11,-12]],"B":[[-1,1,3,5,7]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-1\",\"1\",\"3\",\"5\",\"7\"]],[[\"-8\",\"-9\",\"-10\",\"-11\",\"-12\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0056","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-7], [-5]]、B=[[-2], [-1]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9], [-6]]","explanation_zh":"和矩陣=[[-9], [-6]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071056,"parameters":{"A":[[-7],[-5]],"B":[[-2],[-1]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-2\"],[\"-1\"]],[[\"-7\"],[\"-5\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0057","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-6, -7], [-4, -5]]、B=[[6, 7], [4, 5]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0, 0], [0, 0]]","explanation_zh":"和矩陣=[[0, 0], [0, 0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071057,"parameters":{"A":[[-6,-7],[-4,-5]],"B":[[6,7],[4,5]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-6\",\"-7\"],[\"-4\",\"-5\"]],[[\"6\",\"7\"],[\"4\",\"5\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0058","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-5, -6, -7], [-3, -4, -5]]、B=[[-4, -2, 0], [-3, -1, 1]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7], [-6, -5, -4]]","explanation_zh":"和矩陣=[[-9, -8, -7], [-6, -5, -4]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071058,"parameters":{"A":[[-5,-6,-7],[-3,-4,-5]],"B":[[-4,-2,0],[-3,-1,1]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-4\",\"-2\",\"0\"],[\"-3\",\"-1\",\"1\"]],[[\"-5\",\"-6\",\"-7\"],[\"-3\",\"-4\",\"-5\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0059","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-4, -5, -6, -7], [-2, -3, -4, -5]]、B=[[-5, -3, -1, 1], [-4, -2, 0, 2]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7, -6], [-6, -5, -4, -3]]","explanation_zh":"和矩陣=[[-9, -8, -7, -6], [-6, -5, -4, -3]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071059,"parameters":{"A":[[-4,-5,-6,-7],[-2,-3,-4,-5]],"B":[[-5,-3,-1,1],[-4,-2,0,2]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-4\",\"-5\",\"-6\",\"-7\"],[\"-2\",\"-3\",\"-4\",\"-5\"]],[[\"-5\",\"-3\",\"-1\",\"1\"],[\"-4\",\"-2\",\"0\",\"2\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0060","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-3, -4, -5, -6, -7], [-1, -2, -3, -4, -5]]、B=[[3, 4, 5, 6, 7], [1, 2, 3, 4, 5]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]","explanation_zh":"和矩陣=[[0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071060,"parameters":{"A":[[-3,-4,-5,-6,-7],[-1,-2,-3,-4,-5]],"B":[[3,4,5,6,7],[1,2,3,4,5]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-3\",\"-4\",\"-5\",\"-6\",\"-7\"],[\"-1\",\"-2\",\"-3\",\"-4\",\"-5\"]],[[\"3\",\"4\",\"5\",\"6\",\"7\"],[\"1\",\"2\",\"3\",\"4\",\"5\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0061","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-2], [0], [2]]、B=[[-7], [-6], [-5]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9], [-6], [-3]]","explanation_zh":"和矩陣=[[-9], [-6], [-3]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071061,"parameters":{"A":[[-2],[0],[2]],"B":[[-7],[-6],[-5]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-2\"],[\"0\"],[\"2\"]],[[\"-7\"],[\"-6\"],[\"-5\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0062","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[-1, -2], [1, 0], [3, 2]]、B=[[-8, -6], [-7, -5], [-6, -4]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8], [-6, -5], [-3, -2]]","explanation_zh":"和矩陣=[[-9, -8], [-6, -5], [-3, -2]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071062,"parameters":{"A":[[-1,-2],[1,0],[3,2]],"B":[[-8,-6],[-7,-5],[-6,-4]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-1\",\"-2\"],[\"1\",\"0\"],[\"3\",\"2\"]],[[\"-8\",\"-6\"],[\"-7\",\"-5\"],[\"-6\",\"-4\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0063","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[0, -1, -2], [2, 1, 0], [4, 3, 2]]、B=[[0, 1, 2], [-2, -1, 0], [-4, -3, -2]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0, 0, 0], [0, 0, 0], [0, 0, 0]]","explanation_zh":"和矩陣=[[0, 0, 0], [0, 0, 0], [0, 0, 0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071063,"parameters":{"A":[[0,-1,-2],[2,1,0],[4,3,2]],"B":[[0,1,2],[-2,-1,0],[-4,-3,-2]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"0\",\"-1\",\"-2\"],[\"2\",\"1\",\"0\"],[\"4\",\"3\",\"2\"]],[[\"0\",\"1\",\"2\"],[\"-2\",\"-1\",\"0\"],[\"-4\",\"-3\",\"-2\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0064","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[1, 0, -1, -2], [3, 2, 1, 0], [5, 4, 3, 2]]、B=[[-10, -8, -6, -4], [-9, -7, -5, -3], [-8, -6, -4, -2]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7, -6], [-6, -5, -4, -3], [-3, -2, -1, 0]]","explanation_zh":"和矩陣=[[-9, -8, -7, -6], [-6, -5, -4, -3], [-3, -2, -1, 0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071064,"parameters":{"A":[[1,0,-1,-2],[3,2,1,0],[5,4,3,2]],"B":[[-10,-8,-6,-4],[-9,-7,-5,-3],[-8,-6,-4,-2]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-10\",\"-8\",\"-6\",\"-4\"],[\"-9\",\"-7\",\"-5\",\"-3\"],[\"-8\",\"-6\",\"-4\",\"-2\"]],[[\"1\",\"0\",\"-1\",\"-2\"],[\"3\",\"2\",\"1\",\"0\"],[\"5\",\"4\",\"3\",\"2\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0065","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[2, 1, 0, -1, -2], [4, 3, 2, 1, 0], [6, 5, 4, 3, 2]]、B=[[-11, -9, -7, -5, -3], [-10, -8, -6, -4, -2], [-9, -7, -5, -3, -1]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7, -6, -5], [-6, -5, -4, -3, -2], [-3, -2, -1, 0, 1]]","explanation_zh":"和矩陣=[[-9, -8, -7, -6, -5], [-6, -5, -4, -3, -2], [-3, -2, -1, 0, 1]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071065,"parameters":{"A":[[2,1,0,-1,-2],[4,3,2,1,0],[6,5,4,3,2]],"B":[[-11,-9,-7,-5,-3],[-10,-8,-6,-4,-2],[-9,-7,-5,-3,-1]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-11\",\"-9\",\"-7\",\"-5\",\"-3\"],[\"-10\",\"-8\",\"-6\",\"-4\",\"-2\"],[\"-9\",\"-7\",\"-5\",\"-3\",\"-1\"]],[[\"2\",\"1\",\"0\",\"-1\",\"-2\"],[\"4\",\"3\",\"2\",\"1\",\"0\"],[\"6\",\"5\",\"4\",\"3\",\"2\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0066","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[3], [5], [7], [9]]、B=[[-3], [-5], [-7], [-9]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0], [0], [0], [0]]","explanation_zh":"和矩陣=[[0], [0], [0], [0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071066,"parameters":{"A":[[3],[5],[7],[9]],"B":[[-3],[-5],[-7],[-9]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-3\"],[\"-5\"],[\"-7\"],[\"-9\"]],[[\"3\"],[\"5\"],[\"7\"],[\"9\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0067","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[4, 3], [6, 5], [8, 7], [10, 9]]、B=[[-13, -11], [-12, -10], [-11, -9], [-10, -8]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8], [-6, -5], [-3, -2], [0, 1]]","explanation_zh":"和矩陣=[[-9, -8], [-6, -5], [-3, -2], [0, 1]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071067,"parameters":{"A":[[4,3],[6,5],[8,7],[10,9]],"B":[[-13,-11],[-12,-10],[-11,-9],[-10,-8]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-13\",\"-11\"],[\"-12\",\"-10\"],[\"-11\",\"-9\"],[\"-10\",\"-8\"]],[[\"4\",\"3\"],[\"6\",\"5\"],[\"8\",\"7\"],[\"10\",\"9\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0068","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[5, 4, 3], [7, 6, 5], [9, 8, 7], [11, 10, 9]]、B=[[-14, -12, -10], [-13, -11, -9], [-12, -10, -8], [-11, -9, -7]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7], [-6, -5, -4], [-3, -2, -1], [0, 1, 2]]","explanation_zh":"和矩陣=[[-9, -8, -7], [-6, -5, -4], [-3, -2, -1], [0, 1, 2]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071068,"parameters":{"A":[[5,4,3],[7,6,5],[9,8,7],[11,10,9]],"B":[[-14,-12,-10],[-13,-11,-9],[-12,-10,-8],[-11,-9,-7]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-14\",\"-12\",\"-10\"],[\"-13\",\"-11\",\"-9\"],[\"-12\",\"-10\",\"-8\"],[\"-11\",\"-9\",\"-7\"]],[[\"5\",\"4\",\"3\"],[\"7\",\"6\",\"5\"],[\"9\",\"8\",\"7\"],[\"11\",\"10\",\"9\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0069","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[6, 5, 4, 3], [8, 7, 6, 5], [10, 9, 8, 7], [12, 11, 10, 9]]、B=[[-6, -5, -4, -3], [-8, -7, -6, -5], [-10, -9, -8, -7], [-12, -11, -10, -9]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]","explanation_zh":"和矩陣=[[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071069,"parameters":{"A":[[6,5,4,3],[8,7,6,5],[10,9,8,7],[12,11,10,9]],"B":[[-6,-5,-4,-3],[-8,-7,-6,-5],[-10,-9,-8,-7],[-12,-11,-10,-9]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-6\",\"-5\",\"-4\",\"-3\"],[\"-8\",\"-7\",\"-6\",\"-5\"],[\"-10\",\"-9\",\"-8\",\"-7\"],[\"-12\",\"-11\",\"-10\",\"-9\"]],[[\"6\",\"5\",\"4\",\"3\"],[\"8\",\"7\",\"6\",\"5\"],[\"10\",\"9\",\"8\",\"7\"],[\"12\",\"11\",\"10\",\"9\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0070","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]]、B=[[-16, -14, -12, -10, -8], [-15, -13, -11, -9, -7], [-14, -12, -10, -8, -6], [-13, -11, -9, -7, -5]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7, -6, -5], [-6, -5, -4, -3, -2], [-3, -2, -1, 0, 1], [0, 1, 2, 3, 4]]","explanation_zh":"和矩陣=[[-9, -8, -7, -6, -5], [-6, -5, -4, -3, -2], [-3, -2, -1, 0, 1], [0, 1, 2, 3, 4]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071070,"parameters":{"A":[[7,6,5,4,3],[9,8,7,6,5],[11,10,9,8,7],[13,12,11,10,9]],"B":[[-16,-14,-12,-10,-8],[-15,-13,-11,-9,-7],[-14,-12,-10,-8,-6],[-13,-11,-9,-7,-5]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-16\",\"-14\",\"-12\",\"-10\",\"-8\"],[\"-15\",\"-13\",\"-11\",\"-9\",\"-7\"],[\"-14\",\"-12\",\"-10\",\"-8\",\"-6\"],[\"-13\",\"-11\",\"-9\",\"-7\",\"-5\"]],[[\"7\",\"6\",\"5\",\"4\",\"3\"],[\"9\",\"8\",\"7\",\"6\",\"5\"],[\"11\",\"10\",\"9\",\"8\",\"7\"],[\"13\",\"12\",\"11\",\"10\",\"9\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0071","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[8], [10], [12], [14], [16]]、B=[[-17], [-16], [-15], [-14], [-13]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9], [-6], [-3], [0], [3]]","explanation_zh":"和矩陣=[[-9], [-6], [-3], [0], [3]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071071,"parameters":{"A":[[8],[10],[12],[14],[16]],"B":[[-17],[-16],[-15],[-14],[-13]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-17\"],[\"-16\"],[\"-15\"],[\"-14\"],[\"-13\"]],[[\"8\"],[\"10\"],[\"12\"],[\"14\"],[\"16\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0072","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[9, 8], [11, 10], [13, 12], [15, 14], [17, 16]]、B=[[-9, -8], [-11, -10], [-13, -12], [-15, -14], [-17, -16]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]","explanation_zh":"和矩陣=[[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071072,"parameters":{"A":[[9,8],[11,10],[13,12],[15,14],[17,16]],"B":[[-9,-8],[-11,-10],[-13,-12],[-15,-14],[-17,-16]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-9\",\"-8\"],[\"-11\",\"-10\"],[\"-13\",\"-12\"],[\"-15\",\"-14\"],[\"-17\",\"-16\"]],[[\"9\",\"8\"],[\"11\",\"10\"],[\"13\",\"12\"],[\"15\",\"14\"],[\"17\",\"16\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0073","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[10, 9, 8], [12, 11, 10], [14, 13, 12], [16, 15, 14], [18, 17, 16]]、B=[[-19, -17, -15], [-18, -16, -14], [-17, -15, -13], [-16, -14, -12], [-15, -13, -11]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7], [-6, -5, -4], [-3, -2, -1], [0, 1, 2], [3, 4, 5]]","explanation_zh":"和矩陣=[[-9, -8, -7], [-6, -5, -4], [-3, -2, -1], [0, 1, 2], [3, 4, 5]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071073,"parameters":{"A":[[10,9,8],[12,11,10],[14,13,12],[16,15,14],[18,17,16]],"B":[[-19,-17,-15],[-18,-16,-14],[-17,-15,-13],[-16,-14,-12],[-15,-13,-11]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-19\",\"-17\",\"-15\"],[\"-18\",\"-16\",\"-14\"],[\"-17\",\"-15\",\"-13\"],[\"-16\",\"-14\",\"-12\"],[\"-15\",\"-13\",\"-11\"]],[[\"10\",\"9\",\"8\"],[\"12\",\"11\",\"10\"],[\"14\",\"13\",\"12\"],[\"16\",\"15\",\"14\"],[\"18\",\"17\",\"16\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0074","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[11, 10, 9, 8], [13, 12, 11, 10], [15, 14, 13, 12], [17, 16, 15, 14], [19, 18, 17, 16]]、B=[[-20, -18, -16, -14], [-19, -17, -15, -13], [-18, -16, -14, -12], [-17, -15, -13, -11], [-16, -14, -12, -10]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9, -8, -7, -6], [-6, -5, -4, -3], [-3, -2, -1, 0], [0, 1, 2, 3], [3, 4, 5, 6]]","explanation_zh":"和矩陣=[[-9, -8, -7, -6], [-6, -5, -4, -3], [-3, -2, -1, 0], [0, 1, 2, 3], [3, 4, 5, 6]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071074,"parameters":{"A":[[11,10,9,8],[13,12,11,10],[15,14,13,12],[17,16,15,14],[19,18,17,16]],"B":[[-20,-18,-16,-14],[-19,-17,-15,-13],[-18,-16,-14,-12],[-17,-15,-13,-11],[-16,-14,-12,-10]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-20\",\"-18\",\"-16\",\"-14\"],[\"-19\",\"-17\",\"-15\",\"-13\"],[\"-18\",\"-16\",\"-14\",\"-12\"],[\"-17\",\"-15\",\"-13\",\"-11\"],[\"-16\",\"-14\",\"-12\",\"-10\"]],[[\"11\",\"10\",\"9\",\"8\"],[\"13\",\"12\",\"11\",\"10\"],[\"15\",\"14\",\"13\",\"12\"],[\"17\",\"16\",\"15\",\"14\"],[\"19\",\"18\",\"17\",\"16\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0075","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"同尺寸矩陣相加","stem_zh":"實矩陣，橫列／直行次序固定，A=[[12, 11, 10, 9, 8], [14, 13, 12, 11, 10], [16, 15, 14, 13, 12], [18, 17, 16, 15, 14], [20, 19, 18, 17, 16]]、B=[[-12, -11, -10, -9, -8], [-14, -13, -12, -11, -10], [-16, -15, -14, -13, -12], [-18, -17, -16, -15, -14], [-20, -19, -18, -17, -16]]。明示兩矩陣同尺寸，求 A+B，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]","explanation_zh":"和矩陣=[[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]。只有對應位置相加，不能把不同尺寸補零混合。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["同尺寸矩陣相加"]},"variant":{"family_id":"qf-matrix-addition","seed":202610071075,"parameters":{"A":[[12,11,10,9,8],[14,13,12,11,10],[16,15,14,13,12],[18,17,16,15,14],[20,19,18,17,16]],"B":[[-12,-11,-10,-9,-8],[-14,-13,-12,-11,-10],[-16,-15,-14,-13,-12],[-18,-17,-16,-15,-14],[-20,-19,-18,-17,-16]],"operation":"matrix_addition","domain":"reals","semantic_template":"qf-matrix-addition/{\"inputs\":[[[\"-12\",\"-11\",\"-10\",\"-9\",\"-8\"],[\"-14\",\"-13\",\"-12\",\"-11\",\"-10\"],[\"-16\",\"-15\",\"-14\",\"-13\",\"-12\"],[\"-18\",\"-17\",\"-16\",\"-15\",\"-14\"],[\"-20\",\"-19\",\"-18\",\"-17\",\"-16\"]],[[\"12\",\"11\",\"10\",\"9\",\"8\"],[\"14\",\"13\",\"12\",\"11\",\"10\"],[\"16\",\"15\",\"14\",\"13\",\"12\"],[\"18\",\"17\",\"16\",\"15\",\"14\"],[\"20\",\"19\",\"18\",\"17\",\"16\"]]],\"operation\":\"matrix_addition\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0076","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-12]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-12]]","explanation_zh":"轉置=[[-12]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071076,"parameters":{"M":[[-12]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-12\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0077","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-11, -12]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-11], [-12]]","explanation_zh":"轉置=[[-11], [-12]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071077,"parameters":{"M":[[-11,-12]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-11\",\"-12\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0078","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-10, -11, -12]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-10], [-11], [-12]]","explanation_zh":"轉置=[[-10], [-11], [-12]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071078,"parameters":{"M":[[-10,-11,-12]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-10\",\"-11\",\"-12\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0079","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-9, -10, -11, -12]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-9], [-10], [-11], [-12]]","explanation_zh":"轉置=[[-9], [-10], [-11], [-12]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071079,"parameters":{"M":[[-9,-10,-11,-12]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-9\",\"-10\",\"-11\",\"-12\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0080","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-8, -9, -10, -11, -12]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-8], [-9], [-10], [-11], [-12]]","explanation_zh":"轉置=[[-8], [-9], [-10], [-11], [-12]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071080,"parameters":{"M":[[-8,-9,-10,-11,-12]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-8\",\"-9\",\"-10\",\"-11\",\"-12\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0081","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-7], [-5]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-7, -5]]","explanation_zh":"轉置=[[-7, -5]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071081,"parameters":{"M":[[-7],[-5]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-7\"],[\"-5\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0082","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-6, -7], [-4, -5]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-6, -4], [-7, -5]]","explanation_zh":"轉置=[[-6, -4], [-7, -5]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071082,"parameters":{"M":[[-6,-7],[-4,-5]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-6\",\"-7\"],[\"-4\",\"-5\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0083","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-5, -6, -7], [-3, -4, -5]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-5, -3], [-6, -4], [-7, -5]]","explanation_zh":"轉置=[[-5, -3], [-6, -4], [-7, -5]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071083,"parameters":{"M":[[-5,-6,-7],[-3,-4,-5]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-5\",\"-6\",\"-7\"],[\"-3\",\"-4\",\"-5\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0084","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-4, -5, -6, -7], [-2, -3, -4, -5]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-4, -2], [-5, -3], [-6, -4], [-7, -5]]","explanation_zh":"轉置=[[-4, -2], [-5, -3], [-6, -4], [-7, -5]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071084,"parameters":{"M":[[-4,-5,-6,-7],[-2,-3,-4,-5]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-4\",\"-5\",\"-6\",\"-7\"],[\"-2\",\"-3\",\"-4\",\"-5\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0085","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-3, -4, -5, -6, -7], [-1, -2, -3, -4, -5]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-3, -1], [-4, -2], [-5, -3], [-6, -4], [-7, -5]]","explanation_zh":"轉置=[[-3, -1], [-4, -2], [-5, -3], [-6, -4], [-7, -5]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071085,"parameters":{"M":[[-3,-4,-5,-6,-7],[-1,-2,-3,-4,-5]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-3\",\"-4\",\"-5\",\"-6\",\"-7\"],[\"-1\",\"-2\",\"-3\",\"-4\",\"-5\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0086","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-2], [0], [2]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-2, 0, 2]]","explanation_zh":"轉置=[[-2, 0, 2]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071086,"parameters":{"M":[[-2],[0],[2]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-2\"],[\"0\"],[\"2\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0087","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[-1, -2], [1, 0], [3, 2]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[-1, 1, 3], [-2, 0, 2]]","explanation_zh":"轉置=[[-1, 1, 3], [-2, 0, 2]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071087,"parameters":{"M":[[-1,-2],[1,0],[3,2]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"-1\",\"-2\"],[\"1\",\"0\"],[\"3\",\"2\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0088","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[0, -1, -2], [2, 1, 0], [4, 3, 2]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[0, 2, 4], [-1, 1, 3], [-2, 0, 2]]","explanation_zh":"轉置=[[0, 2, 4], [-1, 1, 3], [-2, 0, 2]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071088,"parameters":{"M":[[0,-1,-2],[2,1,0],[4,3,2]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"0\",\"-1\",\"-2\"],[\"2\",\"1\",\"0\"],[\"4\",\"3\",\"2\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0089","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[1, 0, -1, -2], [3, 2, 1, 0], [5, 4, 3, 2]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[1, 3, 5], [0, 2, 4], [-1, 1, 3], [-2, 0, 2]]","explanation_zh":"轉置=[[1, 3, 5], [0, 2, 4], [-1, 1, 3], [-2, 0, 2]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071089,"parameters":{"M":[[1,0,-1,-2],[3,2,1,0],[5,4,3,2]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"1\",\"0\",\"-1\",\"-2\"],[\"3\",\"2\",\"1\",\"0\"],[\"5\",\"4\",\"3\",\"2\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0090","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[2, 1, 0, -1, -2], [4, 3, 2, 1, 0], [6, 5, 4, 3, 2]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[2, 4, 6], [1, 3, 5], [0, 2, 4], [-1, 1, 3], [-2, 0, 2]]","explanation_zh":"轉置=[[2, 4, 6], [1, 3, 5], [0, 2, 4], [-1, 1, 3], [-2, 0, 2]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071090,"parameters":{"M":[[2,1,0,-1,-2],[4,3,2,1,0],[6,5,4,3,2]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"2\",\"1\",\"0\",\"-1\",\"-2\"],[\"4\",\"3\",\"2\",\"1\",\"0\"],[\"6\",\"5\",\"4\",\"3\",\"2\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0091","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[3], [5], [7], [9]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[3, 5, 7, 9]]","explanation_zh":"轉置=[[3, 5, 7, 9]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071091,"parameters":{"M":[[3],[5],[7],[9]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"3\"],[\"5\"],[\"7\"],[\"9\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0092","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[4, 3], [6, 5], [8, 7], [10, 9]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[4, 6, 8, 10], [3, 5, 7, 9]]","explanation_zh":"轉置=[[4, 6, 8, 10], [3, 5, 7, 9]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071092,"parameters":{"M":[[4,3],[6,5],[8,7],[10,9]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"4\",\"3\"],[\"6\",\"5\"],[\"8\",\"7\"],[\"10\",\"9\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0093","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[5, 4, 3], [7, 6, 5], [9, 8, 7], [11, 10, 9]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[5, 7, 9, 11], [4, 6, 8, 10], [3, 5, 7, 9]]","explanation_zh":"轉置=[[5, 7, 9, 11], [4, 6, 8, 10], [3, 5, 7, 9]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071093,"parameters":{"M":[[5,4,3],[7,6,5],[9,8,7],[11,10,9]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"5\",\"4\",\"3\"],[\"7\",\"6\",\"5\"],[\"9\",\"8\",\"7\"],[\"11\",\"10\",\"9\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0094","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[6, 5, 4, 3], [8, 7, 6, 5], [10, 9, 8, 7], [12, 11, 10, 9]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[6, 8, 10, 12], [5, 7, 9, 11], [4, 6, 8, 10], [3, 5, 7, 9]]","explanation_zh":"轉置=[[6, 8, 10, 12], [5, 7, 9, 11], [4, 6, 8, 10], [3, 5, 7, 9]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071094,"parameters":{"M":[[6,5,4,3],[8,7,6,5],[10,9,8,7],[12,11,10,9]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"6\",\"5\",\"4\",\"3\"],[\"8\",\"7\",\"6\",\"5\"],[\"10\",\"9\",\"8\",\"7\"],[\"12\",\"11\",\"10\",\"9\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0095","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[7, 6, 5, 4, 3], [9, 8, 7, 6, 5], [11, 10, 9, 8, 7], [13, 12, 11, 10, 9]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[7, 9, 11, 13], [6, 8, 10, 12], [5, 7, 9, 11], [4, 6, 8, 10], [3, 5, 7, 9]]","explanation_zh":"轉置=[[7, 9, 11, 13], [6, 8, 10, 12], [5, 7, 9, 11], [4, 6, 8, 10], [3, 5, 7, 9]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071095,"parameters":{"M":[[7,6,5,4,3],[9,8,7,6,5],[11,10,9,8,7],[13,12,11,10,9]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"7\",\"6\",\"5\",\"4\",\"3\"],[\"9\",\"8\",\"7\",\"6\",\"5\"],[\"11\",\"10\",\"9\",\"8\",\"7\"],[\"13\",\"12\",\"11\",\"10\",\"9\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0096","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[8], [10], [12], [14], [16]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[8, 10, 12, 14, 16]]","explanation_zh":"轉置=[[8, 10, 12, 14, 16]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071096,"parameters":{"M":[[8],[10],[12],[14],[16]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"8\"],[\"10\"],[\"12\"],[\"14\"],[\"16\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0097","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[9, 8], [11, 10], [13, 12], [15, 14], [17, 16]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]","explanation_zh":"轉置=[[9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071097,"parameters":{"M":[[9,8],[11,10],[13,12],[15,14],[17,16]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"9\",\"8\"],[\"11\",\"10\"],[\"13\",\"12\"],[\"15\",\"14\"],[\"17\",\"16\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0098","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[10, 9, 8], [12, 11, 10], [14, 13, 12], [16, 15, 14], [18, 17, 16]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[10, 12, 14, 16, 18], [9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]","explanation_zh":"轉置=[[10, 12, 14, 16, 18], [9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071098,"parameters":{"M":[[10,9,8],[12,11,10],[14,13,12],[16,15,14],[18,17,16]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"10\",\"9\",\"8\"],[\"12\",\"11\",\"10\"],[\"14\",\"13\",\"12\"],[\"16\",\"15\",\"14\"],[\"18\",\"17\",\"16\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0099","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[11, 10, 9, 8], [13, 12, 11, 10], [15, 14, 13, 12], [17, 16, 15, 14], [19, 18, 17, 16]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[11, 13, 15, 17, 19], [10, 12, 14, 16, 18], [9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]","explanation_zh":"轉置=[[11, 13, 15, 17, 19], [10, 12, 14, 16, 18], [9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071099,"parameters":{"M":[[11,10,9,8],[13,12,11,10],[15,14,13,12],[17,16,15,14],[19,18,17,16]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"11\",\"10\",\"9\",\"8\"],[\"13\",\"12\",\"11\",\"10\"],[\"15\",\"14\",\"13\",\"12\"],[\"17\",\"16\",\"15\",\"14\"],[\"19\",\"18\",\"17\",\"16\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261006-advance-20261007-r01-matrix-0100","batch_id":"batch-20261006-advance-20261007-r01-matrix-foundations","language":"zh-Hant","source_mko_ids":["mko-matrix"],"title_zh":"矩形矩陣的轉置","stem_zh":"實矩陣，橫列／直行次序固定，M=[[12, 11, 10, 9, 8], [14, 13, 12, 11, 10], [16, 15, 14, 13, 12], [18, 17, 16, 15, 14], [20, 19, 18, 17, 16]]。求轉置 Mᵀ，以巢狀橫列列表回答。","answer":{"kind":"expression","value":"[[12, 14, 16, 18, 20], [11, 13, 15, 17, 19], [10, 12, 14, 16, 18], [9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]","explanation_zh":"轉置=[[12, 14, 16, 18, 20], [11, 13, 15, 17, 19], [10, 12, 14, 16, 18], [9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]。原第 i 橫列、第 j 直行移至第 j 橫列、第 i 直行；矩形尺寸互換。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["矩形矩陣的轉置"]},"variant":{"family_id":"qf-matrix-transpose","seed":202610071100,"parameters":{"M":[[12,11,10,9,8],[14,13,12,11,10],[16,15,14,13,12],[18,17,16,15,14],[20,19,18,17,16]],"operation":"matrix_transpose","domain":"reals","semantic_template":"qf-matrix-transpose/{\"inputs\":[[\"12\",\"11\",\"10\",\"9\",\"8\"],[\"14\",\"13\",\"12\",\"11\",\"10\"],[\"16\",\"15\",\"14\",\"13\",\"12\"],[\"18\",\"17\",\"16\",\"15\",\"14\"],[\"20\",\"19\",\"18\",\"17\",\"16\"]],\"operation\":\"matrix_transpose\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-06","contract_version":"ocme-question-factory-v0.1"}}