Math calculator

Linear System Calculator

Solve small linear systems Ax = b, plus determinant, inverse, and multiply. Same engine as the matrix workspace. Not a CAS. Runs locally.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Specification checked · 10/10 tests · Production surface contract 3/3 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Small Ax=b, det, inverse, multiply, transpose.
Scope: Real matrices
Verification: Engine tested · 10/10 tests · Production surface contract 3/3 · Specification checked · v1.0.0
Named expert review: Optional · Not performed
Specification basis: ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence: 3 golden · 2 boundary · 5 property · Production surface contract 3/3 · Artifact integrity PASS
Production: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract: PASS

Formulas

Core equations used by this calculator.

2×2 determinantdet = a₁₁a₂₂ − a₁₂a₂₁

Solvex = A⁻¹ b when det(A) ≠ 0

iNot a CAS. Not eigenvalue / SVD. Order ≤ 4. Inverse of a singular matrix is SINGULAR_MATRIX.

How to use

Choose solve, det, inverse, multiply, or transpose

Solve needs A and rhs b. Multiply needs square A and B of the same order.

Read x, y (and z) or the matrix

Open /workspace/matrix to keep a local matrix scenario.

Example calculations

Common configurations with formula and result.

2×2

2x + y = 5, x + y = 3

x=2, y=1

unique

det [[1,2],[3,4]]

1·4 − 2·3

−2