Online Gauss-Jordan Calculator

This tool solves systems of linear equations using Gauss-Jordan elimination. Users provide a coefficient matrix A and constants b, either as a full augmented matrix [A|b] or as separate A and b inputs. The backend executes standard row operations: swap rows, scale a row, and replace another row by a multiple. The process yields a reduced row echelon form (RREF) from which the solution set is read.
Conceptual workflow: identify a pivot in each column, normalize to 1, and eliminate all other entries in that column. The tool detects inconsistency when a row of zeros appears with a nonzero constant. If the system is consistent with a unique solution, it returns the solution vector; if there are free variables, it indicates the parametric form and degrees of freedom.
Who benefits: students validating homework, educators preparing checkable exercises, and engineers verifying linear models. Differentiators include safe numeric handling with tolerance for near-zero pivots, clear outputs such as pivot positions and reduced form, and support for small-to-moderate matrices common in classrooms. Core features include automatic dimension inference, error detection for dimension mismatch, exportable results, and quick verification of results for 2x2, 3x3, and up to 10x10 systems.