FA-6068 / Linear algebra / Member archive

Two by two inverse rational · case 03

The adjugate is not divided by the determinant.

Member previewVariant 3 · 3 implementations · 4 checks per implementation

Case contract

Integer matrix/vector entries, rectangular rows, compatible multiplication dimensions, and square matrices for determinant, trace, inverse, symmetry and characteristic-polynomial operations. Rational matrix outputs are reduced Fraction strings. Input is 2 by 2; return None for a singular matrix and otherwise a 2 by 2 list of reduced Fraction strings. Exact operational definition: [[str(Fraction(x,m[0][0]*m[1][1]-m[0][1]*m[1][0])) for x in row] for row in [[m[1][1],-m[0][1]],[-m[1][0],m[0][0]]]] if m[0][0]*m[1][1]!=m[0][1]*m[1][0] else None

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Linear algebra results depend on the stated convention.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
fixture 1: ([[2, 0], [0, 4]],)	`[["4", "0"], ["0", "2"]]`	`[["1/2", "0"], ["0", "1/4"]]`	Failed

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