Explore related knowledge and questions →
← Question derivation index · Original question batch
R0065-33197 · q-20261006-advance-20261007-r01-matrix-0097
The real matrix M=[[9, 8], [11, 10], [13, 12], [15, 14], [17, 16]] is displayed as nested rows. Find Mᵀ as a nested list of rows.
G001 — The real matrix M=[[9, 8], [11, 10], [13, 12], [15, 14], [17, 16]] 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, [[9, 8], [11, 10], [13, 12], [15, 14], [17, 16]]]
After
derived = [5, 2]
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, 9]
After
derived = [1, 1, 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, S002
Before
source roles = [2, 1, 11]
After
derived = [1, 2, 11]
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, 13]
After
derived = [1, 3, 13]
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, 15]
After
derived = [1, 4, 15]
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
Before
source roles = [5, 1, 17]
After
derived = [1, 5, 17]
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, S006
Before
source roles = [1, 2, 8]
After
derived = [2, 1, 8]
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, S007
Before
source roles = [2, 2, 10]
After
derived = [2, 2, 10]
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, S008
Before
source roles = [3, 2, 12]
After
derived = [2, 3, 12]
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, S009
Before
source roles = [4, 2, 14]
After
derived = [2, 4, 14]
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, S010
Before
source roles = [5, 2, 16]
After
derived = [2, 5, 16]
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, S011
S012 · 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.S011 · 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.S010 · 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.S009 · 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.S008 · 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.S007 · 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.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.[[9, 11, 13, 15, 17], [8, 10, 12, 14, 16]]
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: 04cea39f6a037562bafd318088cf2f7e3cfcf5eeeaa3aa4e792940dd8b6a6947candidate record SHA-256: 734974f86f2666da3ec7c7b02c80160cc5d55ff6386e2d1bbfa961acafd4c501semantic review receipt SHA-256: 92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6question-first witness SHA-256: 012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00Lean: NOT_RUN · human review: NOT_PERFORMED