Linear systems

Given a system $A \cdot \mathbf{x} = \mathbf{b}$, this simulator finds all its solutions: it first checks consistency and the number of solutions with the Rouché-Capelli theorem, then looks for shortcuts by eye (evident inconsistencies, immediate particular solutions, relations among the columns), and in any case solves it with Gauss-Jordan on the augmented matrix, all the way to the parametric form of the result. All computations use exact rational arithmetic; the cells of $A$ and $\mathbf{b}$ also accept parameters (for example k or t), with a case analysis on the critical values.

Step 1 — SET THE SYSTEM DIMENSIONS

Equations \((m)\)\(\large\times\)Unknowns \((n)\)

Step 2 — FILL IN THE MATRIX \(A\) AND THE RIGHT-HAND SIDE \(\mathbf{b}\)

We look for ALL solutions of \(A \cdot \mathbf{x}=\mathbf{b}\): shortcuts first, then in any case the standard route with Gauss-Jordan and the parametric form of the result.

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. For the homogeneous system alone and the kernel computation, you can also use the Kernel solver.