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R0065-33191 · q-20261006-advance-20261007-r01-matrix-0091
The real matrix M=[[3], [5], [7], [9]] is displayed as nested rows. Find Mᵀ as a nested list of rows.
G001 — The real matrix M=[[3], [5], [7], [9]] is displayed as nested rows. Find Mᵀ as a nested list of rows.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [qf-matrix-transpose, matrix_transpose, reals, []]
After
derived = [[nested_ROW_matrix]]
Conditions: none
MOD25 uses LOCAL hyphens/named domains,legacy matrices underscores/reals;BASE logic acquires no domain/op.Output tuples,matrices,numeric fields and fraction texts follow THIS source,not a universal/1 rule.Retain originals/English/AST/status.
Rule: R65_SOURCE_bank_keys_operation_domain_ordered_output_roles · Uses: G001
Before
source roles = [M ORIGINAL, [[3], [5], [7], [9]]]
After
derived = [4, 1]
Conditions: none
THIS bank allows1..5 by1..5 matrices,not the R64 2×2 restriction.Type EVERY raw SAFE cell,including unused shape/entry cells.Keep original row order.
Rule: Matrix_RAW_rectangular_1to5_ALL_SAFE_entries_even_unused · Uses: G001, S001
Before
source roles = [1, 1, 3]
After
derived = [1, 1, 3]
Conditions: none
Move EVERY original(i,j)to(j,i),not row reversal or matrix inversion.Rectangular dimensions exchange.
Rule: Matrix_TRANSPOSE_EACH_original_i_j_moves_to_j_i · Uses: G001, S002
Before
source roles = [2, 1, 5]
After
derived = [1, 2, 5]
Conditions: none
Move EVERY original(i,j)to(j,i),not row reversal or matrix inversion.Rectangular dimensions exchange.
Rule: Matrix_TRANSPOSE_EACH_original_i_j_moves_to_j_i · Uses: G001, S003
Before
source roles = [3, 1, 7]
After
derived = [1, 3, 7]
Conditions: none
Move EVERY original(i,j)to(j,i),not row reversal or matrix inversion.Rectangular dimensions exchange.
Rule: Matrix_TRANSPOSE_EACH_original_i_j_moves_to_j_i · Uses: G001, S004
Before
source roles = [4, 1, 9]
After
derived = [1, 4, 9]
Conditions: none
Move EVERY original(i,j)to(j,i),not row reversal or matrix inversion.Rectangular dimensions exchange.
Rule: Matrix_TRANSPOSE_EACH_original_i_j_moves_to_j_i · Uses: G001, S005
S006 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.S005 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.S004 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.S003 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.S002 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.S001 · premise_and_result_audit — Reverse-check ORIGINAL data,types,ordered roles,domain and premises;the conclusion need not uniquely recover its premises.Keep finite source candidates,independent review,formal proof and publication separate.[[3, 5, 7, 9]]
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: abcb5178306f80098a33f50cd16ab014ba353b55616a9f533042bf9eb5d84903candidate record SHA-256: 955283fb582f4d5fc28c86574f05771c1d6ecac4972daa6ee14a51b24001ece1semantic review receipt SHA-256: 92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6question-first witness SHA-256: 012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00Lean: NOT_RUN · human review: NOT_PERFORMED