Row Echelon Form (REF) Solver

Compute the Row Echelon Form1 using Gaussian elimination2 with step-by-step output.
For the fully reduced version, see RREF Solver.

A matrix is in Row Echelon Form (REF) if:

  • All zero rows are at the bottom
  • The first non-zero entry in each row (pivot) is to the right of the pivot in the row above

REF vs RREF:3

  • REF only requires forward elimination (Gaussian elimination)
  • RREF additionally requires back-substitution (Gauss-Jordan elimination)
  • RREF has pivots = 1 and zeros above each pivot; REF does not

Uses:

  • Solving systems via back-substitution4
  • Computing determinants (product of pivots times sign from swaps)
  • Determining rank and linear independence
Set matrix dimensions

Enter dimensions and click Generate Matrix to create the input grid.

Display values as:
1 — Set Up
Loads a pre-filled 3×4 augmented matrix — ready to reduce.
2 — Compute
Performs Gaussian elimination with partial pivoting to row echelon form.
Resets all dimensions, matrix entries, and results.