RREF Calculator
Paste a matrix (optionally augmented with a constants column) and watch Gauss-Jordan elimination move by move — each row operation written out, each pivot highlighted.
One row per line of boxes. The last column is the constants when augmented.
Every variable is a pivot variable, so the system pins down a single solution: x1 = -4, x2 = 4.5.
Entries within 0.000000001 of an integer are snapped to it, so textbook systems come out exact.
Start with the matrix
The last column holds the constants (the augmented column) — row operations keep the system's solutions unchanged.
1 2 5 3 4 6 Pivot 1: make a 1 in column 1, clear the rest of it
R1 ↔ R2 · R1 → R1 ÷ 3 · R2 → R2 − 1·R1
R1 ↔ R2R1 → R1 ÷ 3R2 → R2 − 1·R11 1.3333 2 0 0.6667 3 Pivot 2: make a 1 in column 2, clear the rest of it
R2 → R2 ÷ 0.6667 · R1 → R1 − 1.3333·R2
R2 → R2 ÷ 0.6667R1 → R1 − 1.3333·R21 0 -4 0 1 4.5 Read the solution from the last column
Each row now says xᵢ = constant directly.
- x1
- -4
- x2
- 4.5
Works instantly in your browser — nothing is uploaded, and the URL keeps your numbers so you can share the exact worked example.
Studying statistics or linear algebra? See every tool in the Stats & Algebra hub — variance, interpolation, RREF and eigenvectors, cross-linked.Why Gauss-Jordan?
Row reduction is the workhorse of linear algebra: solving systems, finding inverses, computing rank, testing independence. The “Jordan” half — clearing entries above each pivot as well as below — is what makes the final read-off trivial, and it is exactly what this calculator shows.