Kernel / null space of a linear map

Given a matrix $A$, this simulator solves the homogeneous system $A \cdot \mathbf{x} = \mathbf{0}$ and finds its kernel: it first looks for simple relations among the columns, then solves the system with Gauss-Jordan anyway and compares the two results. All computations use exact rational arithmetic; the cells also accept parameters (for example k), with a case analysis on the critical values.

Step 1 — SET THE MATRIX DIMENSIONS

Rows \((m)\)\(\large\times\)Columns \((n)\)

Step 2 — FILL IN THE MATRIX \(A\) (numbers or parameters)

We look for the solutions of the HOMOGENEOUS system, i.e. the kernel: the vectors \(\mathbf{x}\) with \(A \cdot \mathbf{x}=\mathbf{0}\).

RESET VALUESRANDOM VALUESQUICK RESULT

STEP-BY-STEP SOLUTION

See also

For the detailed, move-by-move row reduction of a matrix, use the Gauss-Jordan solver.