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Question 33153: Dimensions of a Nonempty Matrix

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0065-33153 · q-20261006-advance-20261007-r01-matrix-0003

Original question and givens

The real matrix M=[[-10, -11, -12]] is displayed as nested rows. Each dimension is from one through five. Give (number of rows, number of columns).

  • G001 — The real matrix M=[[-10, -11, -12]] is displayed as nested rows. Each dimension is from one through five. Give (number of rows, number of columns).

Definition and scope

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.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-matrix-shape, matrix_shape, reals, []]

After

derived = [[rows_columns_NUMBER_pair]]

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.

Step identifiers and dependencies

Rule: R65_SOURCE_bank_keys_operation_domain_ordered_output_roles · Uses: G001

S002 · implies

Before

source roles = [M ORIGINAL, [[-10, -11, -12]]]

After

derived = [1, 3]

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.

Step identifiers and dependencies

Rule: Matrix_RAW_rectangular_1to5_ALL_SAFE_entries_even_unused · Uses: G001, S001

S003 · implies

Before

source roles = [[[-10, -11, -12]]]

After

derived = [1, 3, 3]

Conditions: none

Count rows FIRST,then columns per row.Shape is(m,n),not(n,m)or total entries.

Step identifiers and dependencies

Rule: Matrix_SHAPE_rows_THEN_columns_NOT_total_entries · Uses: G001, S002

Reverse checks

  • 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.

Result

(1, 3)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 7142bb1737b34ff50492334390042e21172d7048fc1d60aafa5a291a143a2260
  • candidate record SHA-256: 902ae704afbb417511327fe3238c9c828bf0a5370d68118e05d56b1ce85bb21e
  • semantic review receipt SHA-256: 92bb5fa69818f30cd2806d74a26bd5ede6c48c80d2ecc3d31a5130d4ad7666b6
  • question-first witness SHA-256: 012b5aa905280d616be49aa9462daaa73bf7f6247d0a796e78bc5bcd24e6bd00
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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