本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261014-advance-20261102-r03-linear-map-image-foundations · 2026-10-14 · 100 題
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,1],[2,2]],"target":[2,4]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([2, 4], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([2, 4], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,2],[2,4]],"target":[3,6]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([3, 6], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([3, 6], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,3],[2,6]],"target":[4,8]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([4, 8], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([4, 8], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,4],[2,8]],"target":[5,10]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([5, 10], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([5, 10], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,5],[2,10]],"target":[6,12]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([6, 12], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([6, 12], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,6],[2,12]],"target":[7,14]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([7, 14], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([7, 14], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,7],[2,14]],"target":[8,16]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([8, 16], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([8, 16], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,8],[2,16]],"target":[9,18]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([9, 18], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([9, 18], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,9],[2,18]],"target":[10,20]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([10, 20], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([10, 20], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,10],[2,20]],"target":[11,22]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([11, 22], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([11, 22], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,11],[2,22]],"target":[12,24]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([12, 24], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([12, 24], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,12],[2,24]],"target":[13,26]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([13, 26], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([13, 26], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,13],[2,26]],"target":[14,28]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([14, 28], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([14, 28], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,14],[2,28]],"target":[15,30]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([15, 30], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([15, 30], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,15],[2,30]],"target":[16,32]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([16, 32], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([16, 32], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,16],[2,32]],"target":[17,34]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([17, 34], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([17, 34], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,17],[2,34]],"target":[18,36]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([18, 36], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([18, 36], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,18],[2,36]],"target":[19,38]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([19, 38], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([19, 38], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,19],[2,38]],"target":[20,40]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([20, 40], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([20, 40], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,20],[2,40]],"target":[21,42]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([21, 42], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([21, 42], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,21],[2,42]],"target":[22,44]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([22, 44], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([22, 44], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,22],[2,44]],"target":[23,46]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([23, 46], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([23, 46], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,23],[2,46]],"target":[24,48]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([24, 48], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([24, 48], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,24],[2,48]],"target":[25,50]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([25, 50], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([25, 50], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-membership；資料={"matrix":[[1,25],[2,50]],"target":[26,52]}。請依 [target,rank,image_basis,in_image,certificate] 欄序回答。
([26, 52], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])
Wave5第二層核對=([26, 52], 1, [[1, 2]], 是, [column_span_cross, [1, 2], 0])；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-membership · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,1],[2,2]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 1], [2, 2]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 1], [2, 2]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,2],[2,4]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 2], [2, 4]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 2], [2, 4]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,3],[2,6]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 3], [2, 6]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 3], [2, 6]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,4],[2,8]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 4], [2, 8]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 4], [2, 8]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,5],[2,10]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 5], [2, 10]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 5], [2, 10]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,6],[2,12]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 6], [2, 12]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 6], [2, 12]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,7],[2,14]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 7], [2, 14]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 7], [2, 14]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,8],[2,16]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 8], [2, 16]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 8], [2, 16]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,9],[2,18]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 9], [2, 18]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 9], [2, 18]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,10],[2,20]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 10], [2, 20]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 10], [2, 20]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,11],[2,22]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 11], [2, 22]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 11], [2, 22]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,12],[2,24]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 12], [2, 24]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 12], [2, 24]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,13],[2,26]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 13], [2, 26]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 13], [2, 26]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,14],[2,28]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 14], [2, 28]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 14], [2, 28]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,15],[2,30]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 15], [2, 30]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 15], [2, 30]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,16],[2,32]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 16], [2, 32]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 16], [2, 32]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,17],[2,34]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 17], [2, 34]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 17], [2, 34]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,18],[2,36]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 18], [2, 36]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 18], [2, 36]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,19],[2,38]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 19], [2, 38]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 19], [2, 38]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,20],[2,40]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 20], [2, 40]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 20], [2, 40]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,21],[2,42]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 21], [2, 42]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 21], [2, 42]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,22],[2,44]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 22], [2, 44]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 22], [2, 44]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,23],[2,46]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 23], [2, 46]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 23], [2, 46]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,24],[2,48]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 24], [2, 48]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 24], [2, 48]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-basis；資料={"matrix":[[1,25],[2,50]]}。請依 [matrix,rank,image_basis,certificate] 欄序回答。
([[1, 25], [2, 50]], 1, [[1, 2]], full_real_column_span)
Wave5第二層核對=([[1, 25], [2, 50]], 1, [[1, 2]], full_real_column_span)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-basis · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,1],[2,2]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,2],[2,4]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,3],[2,6]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,4],[2,8]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,5],[2,10]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,6],[2,12]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,7],[2,14]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,8],[2,16]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,9],[2,18]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,10],[2,20]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,11],[2,22]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,12],[2,24]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,13],[2,26]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,14],[2,28]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,15],[2,30]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,16],[2,32]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,17],[2,34]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,18],[2,36]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,19],[2,38]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,20],[2,40]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,21],[2,42]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,22],[2,44]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,23],[2,46]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,24],[2,48]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-rank；資料={"matrix":[[1,25],[2,50]]}。請依 [rank,basis_count,equal] 欄序回答。
(1, 1, 是)
Wave5第二層核對=(1, 1, 是)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-rank · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[1,1],"bound":1}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([1, 1], 1, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([1, 1], 1, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[3,1],"bound":2}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([3, 1], 2, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([3, 1], 2, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[5,1],"bound":3}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([5, 1], 3, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([5, 1], 3, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[7,1],"bound":4}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([7, 1], 4, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([7, 1], 4, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[9,1],"bound":5}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([9, 1], 5, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([9, 1], 5, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[11,1],"bound":1}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([11, 1], 1, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([11, 1], 1, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[13,1],"bound":2}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([13, 1], 2, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([13, 1], 2, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[15,1],"bound":3}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([15, 1], 3, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([15, 1], 3, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[17,1],"bound":4}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([17, 1], 4, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([17, 1], 4, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[19,1],"bound":5}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([19, 1], 5, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([19, 1], 5, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[21,1],"bound":1}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([21, 1], 1, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([21, 1], 1, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[23,1],"bound":2}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([23, 1], 2, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([23, 1], 2, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[25,1],"bound":3}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([25, 1], 3, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([25, 1], 3, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[27,1],"bound":4}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([27, 1], 4, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([27, 1], 4, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[29,1],"bound":5}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([29, 1], 5, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([29, 1], 5, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[31,1],"bound":1}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([31, 1], 1, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([31, 1], 1, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[33,1],"bound":2}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([33, 1], 2, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([33, 1], 2, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[35,1],"bound":3}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([35, 1], 3, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([35, 1], 3, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[37,1],"bound":4}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([37, 1], 4, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([37, 1], 4, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[39,1],"bound":5}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([39, 1], 5, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([39, 1], 5, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[41,1],"bound":1}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([41, 1], 1, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([41, 1], 1, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[43,1],"bound":2}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([43, 1], 2, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([43, 1], 2, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[45,1],"bound":3}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([45, 1], 3, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([45, 1], 3, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[47,1],"bound":4}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([47, 1], 4, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([47, 1], 4, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate
同一精確2×2線性映射與column-span證書。操作=image-bounded-search-boundary；資料={"matrix":[[2,0],[0,2]],"target":[49,1],"bound":5}。請依 [target,bound,integer_witnesses,global_membership,boundary] 欄序回答。
([49, 1], 5, [], 是, bounded_failure_not_global_nonmembership)
Wave5第二層核對=([49, 1], 5, [], 是, bounded_failure_not_global_nonmembership)；依完整明示資料重算；image是full-real column span且不等同codomain；bounded fiber search失敗不證全域nonmembership。
線性映射的像 · qf-mod33-image-bounded-search-boundary · candidate