Matrix toolkit

Exact row reduction, with the determinant, inverse, and nullspace derived from it. Solving a system uses the same augmented matrix.

Reading the output

Each step shows the whole matrix after an operation, with the pivot boxed. Entries stay as exact fractions, so the result matches a hand calculation.

Operations

Row reduce gives the reduced row echelon form, the rank, the pivot columns, and the nullity.
Determinant uses elimination and tracks the sign.
Inverse row-reduces $[A \mid I]$ and reports when $A$ is singular.
Nullspace reads a basis from the free columns of the reduced matrix.
Solve row-reduces $[A \mid \mathbf{b}]$ and distinguishes a unique solution, infinitely many solutions, and an inconsistent system.

Export

The $\LaTeX$ tab previews the working and lets you copy or download the .tex source. The document uses amsmath and bmatrix, so a standard TeX installation compiles it.