Mathematics / Free calculator

Linear systems Ax = b

Solve a linear system with exact rational row reduction and identify unique, inconsistent, or underdetermined systems.

01 Your inputs

1–7 rows and columns. Entries may be exact integers, decimals, or fractions; separate with spaces or commas.

One value per row; same row count as A.

Calculated on your device. Inputs are not transmitted or stored.

02 Your result

Enter your values and select Calculate.

The method

Ax=b

A worked example

For A = [1 2; 3 4] and b = [5; 11], x = [1; 2]. Substitution gives Ax = b exactly.

Assumptions & limits

Solve up to 7 equations with 7 unknowns using exact fractions or finite decimals. Free variables describe infinitely many solutions; an inconsistent row means there is no solution. Rational numerators and denominators must stay below 260 digits, and scientific notation exponents are limited to ±15.

Calculation source: Math Workbench: exact rational row reduction.

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