# Question 7863: Reversible Row Addition and Before/After Classification

[Return to catalogue page 40](https://ocme.evemisslab.com/en/questions/page/40/)

[← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261012-advance-20261016-r05-system-linear-equations-foundations/#q-20261012-advance-20261016-r05-system-linear-equations-0063)

This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0014-07863 · q-20261012-advance-20261016-r05-system-linear-equations-0063



## Original question and givens

Over R, rows=[[1, 0, 0], [0, 1, 2]], where each [a,b,c] means a*x+b*y=c. t=-1; replace only row2 by row2+t*row1, including its right-side constant. Give (new rows, original classification record [signed D, rankA, rankAb, no-solution/unique-solution/infinitely-many-solutions, ordered rational solution [x,y] or not-applicable/not-unique], new classification record, invertible-row-operation eligibility).


- G001 — Over R, rows=[[1, 0, 0], [0, 1, 2]], where each [a,b,c] means a*x+b*y=c. t=-1; replace only row2 by row2+t*row1, including its right-side constant. Give (new rows, original classification record [signed D, rankA, rankAb, no-solution/unique-solution/infinitely-many-solutions, ordered rational solution [x,y] or not-applicable/not-unique], new classification record, invertible-row-operation eligibility).





## 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.


- [mko-system-linear-equations](https://ocme.evemisslab.com/en/mko/mko-system-linear-equations/)





## Step-by-step derivation

S001 · impliesBefore

rows=[[1, 0, 0], [0, 1, 2]]

After

each row [a,b,c] means a*x+b*y=c over R

Conditions: none

Both equations must hold simultaneously.The right-hand constant is not a third unknown.Retain degenerate zero-coefficient rows rather than presuming a nonzero determinant.

Step identifiers and dependenciesRule: two_equations_real_system_scope · Uses: G001





S002 · calculationBefore

before ae := mul(1, 1)

After

before ae = 1

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S001





S003 · calculationBefore

before bd := mul(0, 0)

After

before bd = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S002





S004 · calculationBefore

before D := sub(1, 0)

After

before D = 1

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S003





S005 · calculationBefore

before af := mul(1, 2)

After

before af = 2

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S004





S006 · calculationBefore

before cd := mul(0, 0)

After

before cd = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S005





S007 · calculationBefore

before minor_x_rhs := sub(2, 0)

After

before minor_x_rhs = 2

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S006





S008 · calculationBefore

before bf := mul(0, 2)

After

before bf = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S007





S009 · calculationBefore

before ce := mul(0, 1)

After

before ce = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S008





S010 · calculationBefore

before minor_y_rhs := sub(0, 0)

After

before minor_y_rhs = 0

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S009





S011 · impliesBefore

phase=before;rows=[[1, 0, 0], [0, 1, 2]];2x2 minors=[1, 2, 0]

After

rankA=2;rankAb=2

Conditions: none

A nonzero coefficient 2×2 minor gives rank2;otherwise a nonzero coefficient gives rank1.The augmented matrix has three 2×2 minors;if all vanish,check its entries,including the right-hand constants.

Step identifiers and dependenciesRule: system_rank_from_complete_minors · Uses: G001, S010





S012 · calculationBefore

before x numerator := sub(0, 0)

After

before x numerator = 0

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S011





S013 · calculationBefore

before x solution := div(0, 1)

After

before x solution = 0

Conditions: none

The denominator has separately been checked nonzero;divide exactly as a rational number.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S012





S014 · calculationBefore

before y solution := div(2, 1)

After

before y solution = 2

Conditions: none

The denominator has separately been checked nonzero;divide exactly as a rational number.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S013





S015 · calculationBefore

before solution row0 ax := mul(1, 0)

After

before solution row0 ax = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S014





S016 · calculationBefore

before solution row0 by := mul(0, 2)

After

before solution row0 by = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S015





S017 · calculationBefore

before solution row0 lhs := sum(0, 0)

After

before solution row0 lhs = 0

Conditions: none

Add the already aligned component or position,without mixing coordinates.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S016





S018 · calculationBefore

before solution row0 residual := sub(0, 0)

After

before solution row0 residual = 0

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S017





S019 · calculationBefore

before solution row1 ax := mul(0, 0)

After

before solution row1 ax = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S018





S020 · calculationBefore

before solution row1 by := mul(1, 2)

After

before solution row1 by = 2

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S019





S021 · calculationBefore

before solution row1 lhs := sum(0, 2)

After

before solution row1 lhs = 2

Conditions: none

Add the already aligned component or position,without mixing coordinates.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S020





S022 · calculationBefore

before solution row1 residual := sub(2, 2)

After

before solution row1 residual = 0

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S021





S023 · impliesBefore

phase=before;D=1;D*x=0;D*y=2

After

solution=[0/1, 2/1];row residuals=[0, 0]

Conditions: none

Nonzero D permits division after Cramer elimination:D·x=ce−bf and D·y=af−cd.Substitute the rational pair into both original rows;both residuals are zero.Nonzero D also ensures uniqueness.

Step identifiers and dependenciesRule: system_unique_solution_substitution · Uses: G001, S022





S024 · impliesBefore

phase=before;rankA=2;rankAb=2;unknowns=2

After

class=unique solution;solution/status=[0/1, 2/1]

Conditions: none

Unequal ranks mean an inconsistent row and no solution.Equal rank below2 leaves a free variable and infinitely many real solutions.Only rank2 gives a unique solution.Never divide by D when D=0.

Step identifiers and dependenciesRule: system_consistency_and_free_variables · Uses: G001, S023





S025 · calculationBefore

t row1[0] := mul(-1, 1)

After

t row1[0] = -1

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S024





S026 · calculationBefore

t row1[1] := mul(-1, 0)

After

t row1[1] = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S025





S027 · calculationBefore

t row1[2] := mul(-1, 0)

After

t row1[2] = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S026





S028 · calculationBefore

row2+t row1[0] := sum(0, -1)

After

row2+t row1[0] = -1

Conditions: none

Add the already aligned component or position,without mixing coordinates.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S027





S029 · calculationBefore

row2+t row1[1] := sum(1, 0)

After

row2+t row1[1] = 1

Conditions: none

Add the already aligned component or position,without mixing coordinates.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S028





S030 · calculationBefore

row2+t row1[2] := sum(2, 0)

After

row2+t row1[2] = 2

Conditions: none

Add the already aligned component or position,without mixing coordinates.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S029





S031 · impliesBefore

operation=system-eliminate-row;t=-1;old rows=[[1, 0, 0], [0, 1, 2]]

After

new rows=[[1, 0, 0], [-1, 1, 2]];invertible=Yes;inverse=row2 -> row2-(-1)*row1

Conditions: none

A row operation includes the right-hand constant.Adding any t times the other row is undone by adding−t times it.Scaling can be divided back only for t≠0.At t=0 a redundant system may coincidentally keep its solution set,but the operation is still not invertible.

Step identifiers and dependenciesRule: row_operation_inverse_guard · Uses: G001, S030





S032 · calculationBefore

after ae := mul(1, 1)

After

after ae = 1

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S031





S033 · calculationBefore

after bd := mul(0, -1)

After

after bd = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S032





S034 · calculationBefore

after D := sub(1, 0)

After

after D = 1

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S033





S035 · calculationBefore

after af := mul(1, 2)

After

after af = 2

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S034





S036 · calculationBefore

after cd := mul(0, -1)

After

after cd = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S035





S037 · calculationBefore

after minor_x_rhs := sub(2, 0)

After

after minor_x_rhs = 2

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S036





S038 · calculationBefore

after bf := mul(0, 2)

After

after bf = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S037





S039 · calculationBefore

after ce := mul(0, 1)

After

after ce = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S038





S040 · calculationBefore

after minor_y_rhs := sub(0, 0)

After

after minor_y_rhs = 0

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S039





S041 · impliesBefore

phase=after;rows=[[1, 0, 0], [-1, 1, 2]];2x2 minors=[1, 2, 0]

After

rankA=2;rankAb=2

Conditions: none

A nonzero coefficient 2×2 minor gives rank2;otherwise a nonzero coefficient gives rank1.The augmented matrix has three 2×2 minors;if all vanish,check its entries,including the right-hand constants.

Step identifiers and dependenciesRule: system_rank_from_complete_minors · Uses: G001, S040





S042 · calculationBefore

after x numerator := sub(0, 0)

After

after x numerator = 0

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S041





S043 · calculationBefore

after x solution := div(0, 1)

After

after x solution = 0

Conditions: none

The denominator has separately been checked nonzero;divide exactly as a rational number.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S042





S044 · calculationBefore

after y solution := div(2, 1)

After

after y solution = 2

Conditions: none

The denominator has separately been checked nonzero;divide exactly as a rational number.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S043





S045 · calculationBefore

after solution row0 ax := mul(1, 0)

After

after solution row0 ax = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S044





S046 · calculationBefore

after solution row0 by := mul(0, 2)

After

after solution row0 by = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S045





S047 · calculationBefore

after solution row0 lhs := sum(0, 0)

After

after solution row0 lhs = 0

Conditions: none

Add the already aligned component or position,without mixing coordinates.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S046





S048 · calculationBefore

after solution row0 residual := sub(0, 0)

After

after solution row0 residual = 0

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S047





S049 · calculationBefore

after solution row1 ax := mul(-1, 0)

After

after solution row1 ax = 0

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S048





S050 · calculationBefore

after solution row1 by := mul(1, 2)

After

after solution row1 by = 2

Conditions: none

Multiply the specified scalar and component at this position;do not substitute an inner product or entrywise matrix product.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S049





S051 · calculationBefore

after solution row1 lhs := sum(0, 2)

After

after solution row1 lhs = 2

Conditions: none

Add the already aligned component or position,without mixing coordinates.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S050





S052 · calculationBefore

after solution row1 residual := sub(2, 2)

After

after solution row1 residual = 0

Conditions: none

Subtract the second operand from the first in the requested order,retaining the residual sign.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S051





S053 · impliesBefore

phase=after;D=1;D*x=0;D*y=2

After

solution=[0/1, 2/1];row residuals=[0, 0]

Conditions: none

Nonzero D permits division after Cramer elimination:D·x=ce−bf and D·y=af−cd.Substitute the rational pair into both original rows;both residuals are zero.Nonzero D also ensures uniqueness.

Step identifiers and dependenciesRule: system_unique_solution_substitution · Uses: G001, S052





S054 · impliesBefore

phase=after;rankA=2;rankAb=2;unknowns=2

After

class=unique solution;solution/status=[0/1, 2/1]

Conditions: none

Unequal ranks mean an inconsistent row and no solution.Equal rank below2 leaves a free variable and infinitely many real solutions.Only rank2 gives a unique solution.Never divide by D when D=0.

Step identifiers and dependenciesRule: system_consistency_and_free_variables · Uses: G001, S053









## Reverse checks


- S054 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S053 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S052 · premise_and_result_audit — Recompute after solution row1 residual with exact rational arithmetic, not rounded decimals.
- S051 · premise_and_result_audit — Recompute after solution row1 lhs with exact rational arithmetic, not rounded decimals.
- S050 · premise_and_result_audit — Recompute after solution row1 by with exact rational arithmetic, not rounded decimals.
- S049 · premise_and_result_audit — Recompute after solution row1 ax with exact rational arithmetic, not rounded decimals.
- S048 · premise_and_result_audit — Recompute after solution row0 residual with exact rational arithmetic, not rounded decimals.
- S047 · premise_and_result_audit — Recompute after solution row0 lhs with exact rational arithmetic, not rounded decimals.
- S046 · premise_and_result_audit — Recompute after solution row0 by with exact rational arithmetic, not rounded decimals.
- S045 · premise_and_result_audit — Recompute after solution row0 ax with exact rational arithmetic, not rounded decimals.
- S044 · premise_and_result_audit — Recompute after y solution with exact rational arithmetic, not rounded decimals.
- S043 · premise_and_result_audit — Recompute after x solution with exact rational arithmetic, not rounded decimals.
- S042 · premise_and_result_audit — Recompute after x numerator with exact rational arithmetic, not rounded decimals.
- S041 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S040 · premise_and_result_audit — Recompute after minor_y_rhs with exact rational arithmetic, not rounded decimals.
- S039 · premise_and_result_audit — Recompute after ce with exact rational arithmetic, not rounded decimals.
- S038 · premise_and_result_audit — Recompute after bf with exact rational arithmetic, not rounded decimals.
- S037 · premise_and_result_audit — Recompute after minor_x_rhs with exact rational arithmetic, not rounded decimals.
- S036 · premise_and_result_audit — Recompute after cd with exact rational arithmetic, not rounded decimals.
- S035 · premise_and_result_audit — Recompute after af with exact rational arithmetic, not rounded decimals.
- S034 · premise_and_result_audit — Recompute after D with exact rational arithmetic, not rounded decimals.
- S033 · premise_and_result_audit — Recompute after bd with exact rational arithmetic, not rounded decimals.
- S032 · premise_and_result_audit — Recompute after ae with exact rational arithmetic, not rounded decimals.
- S031 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S030 · premise_and_result_audit — Recompute row2+t row1[2] with exact rational arithmetic, not rounded decimals.
- S029 · premise_and_result_audit — Recompute row2+t row1[1] with exact rational arithmetic, not rounded decimals.
- S028 · premise_and_result_audit — Recompute row2+t row1[0] with exact rational arithmetic, not rounded decimals.
- S027 · premise_and_result_audit — Recompute t row1[2] with exact rational arithmetic, not rounded decimals.
- S026 · premise_and_result_audit — Recompute t row1[1] with exact rational arithmetic, not rounded decimals.
- S025 · premise_and_result_audit — Recompute t row1[0] with exact rational arithmetic, not rounded decimals.
- S024 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S023 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S022 · premise_and_result_audit — Recompute before solution row1 residual with exact rational arithmetic, not rounded decimals.
- S021 · premise_and_result_audit — Recompute before solution row1 lhs with exact rational arithmetic, not rounded decimals.
- S020 · premise_and_result_audit — Recompute before solution row1 by with exact rational arithmetic, not rounded decimals.
- S019 · premise_and_result_audit — Recompute before solution row1 ax with exact rational arithmetic, not rounded decimals.
- S018 · premise_and_result_audit — Recompute before solution row0 residual with exact rational arithmetic, not rounded decimals.
- S017 · premise_and_result_audit — Recompute before solution row0 lhs with exact rational arithmetic, not rounded decimals.
- S016 · premise_and_result_audit — Recompute before solution row0 by with exact rational arithmetic, not rounded decimals.
- S015 · premise_and_result_audit — Recompute before solution row0 ax with exact rational arithmetic, not rounded decimals.
- S014 · premise_and_result_audit — Recompute before y solution with exact rational arithmetic, not rounded decimals.
- S013 · premise_and_result_audit — Recompute before x solution with exact rational arithmetic, not rounded decimals.
- S012 · premise_and_result_audit — Recompute before x numerator with exact rational arithmetic, not rounded decimals.
- S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
- S010 · premise_and_result_audit — Recompute before minor_y_rhs with exact rational arithmetic, not rounded decimals.
- S009 · premise_and_result_audit — Recompute before ce with exact rational arithmetic, not rounded decimals.
- S008 · premise_and_result_audit — Recompute before bf with exact rational arithmetic, not rounded decimals.
- S007 · premise_and_result_audit — Recompute before minor_x_rhs with exact rational arithmetic, not rounded decimals.
- S006 · premise_and_result_audit — Recompute before cd with exact rational arithmetic, not rounded decimals.
- S005 · premise_and_result_audit — Recompute before af with exact rational arithmetic, not rounded decimals.
- S004 · premise_and_result_audit — Recompute before D with exact rational arithmetic, not rounded decimals.
- S003 · premise_and_result_audit — Recompute before bd with exact rational arithmetic, not rounded decimals.
- S002 · premise_and_result_audit — Recompute before ae with exact rational arithmetic, not rounded decimals.
- S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.





## Result

([[1, 0, 0], [-1, 1, 2]], [1, 2, 2, unique-solution, [0/1, 2/1]], [1, 2, 2, unique-solution, [0/1, 2/1]], Yes)

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: f0a9c808b7a70e08e7d2b1e33be2fe3a33ff95fd13edaabe7c73fc24417ec7d8
- candidate record SHA-256: 630ad51c0695a1e1a6939897a365c65215d8045f96135f6621e435efb2e58349
- semantic review receipt SHA-256: 23ba8196e85a09c03add0a87f96bec5d67a00dc648d1d68eef89101525b41a77
- question-first witness SHA-256: 17d59afc327b7cb8b6e588686d6dc1abbccd384d8ba32b8c046652f96821d705
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261012-advance-20261016-r05-system-linear-equations-0063.json)