Solve a Linear System (Ax = b)
Enter the coefficient matrix A and the right-hand side vector b. The calculator builds the augmented matrix [A | b], reduces it with Gauss-Jordan elimination, and reports a unique solution, no solution, or infinitely many solutions with a parametric form.
Frequently asked questions
How does the calculator detect no solution?
If the reduced row echelon form contains a row of the form [0 0 … 0 | c] with c ≠ 0, the system is inconsistent and has no solution.
When are there infinitely many solutions?
When the system is consistent but has fewer pivot columns than variables — the variables without pivots are free, giving a parametric family.
Does this require a square matrix?
No. The method works for any m×n system. Over- and under-determined systems are handled equally well.