Reduced Row Echelon Form (RREF) Solver

Compute the Reduced Row Echelon Form1 of a matrix using Gauss-Jordan elimination2 with detailed step-by-step output.
Useful for solving systems of linear equations, finding matrix rank, and determining linear independence.

A matrix is in Reduced Row Echelon Form (RREF) if it satisfies:

  • All zero rows are at the bottom
  • The first non-zero entry in each row (pivot) is 1
  • Each pivot is to the right of the pivot in the row above (staircase pattern)3
  • Each pivot is the only non-zero entry in its column

Uses:

  • Solving systems of linear equations \(Ax = b\)
  • Finding the rank of a matrix
  • Determining linear independence of vectors
  • Finding basis for row space and null space4
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 step-by-step Gauss–Jordan elimination to reduced row echelon form.
Resets all dimensions, matrix entries, and results.