Gauss-Jordan Elimination Calculator

Solve a 2x2 or 3x3 linear system by reducing the augmented matrix [A|b] to reduced row echelon form (RREF) with partial pivoting.

Frequently Asked Questions

How is Gauss-Jordan elimination different from Gauss elimination?

Gauss elimination stops at row echelon form and uses back-substitution. Gauss-Jordan continues to reduced row echelon form so the variables can be read off directly.

What happens when the system has no solution?

After row reduction one row becomes 0 = nonzero, an impossibility. The system is inconsistent.

When is the solution not unique?

When a row of A becomes all zero and the matching b entry is also zero. The free variables generate an infinite family of solutions.

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Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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