Row Echelon Form Calculator

Convert any matrix to row echelon form (REF) using Gaussian elimination.

How It Works

Enter any matrix. Gaussian forward elimination produces row echelon form where all entries below each pivot are zero and pivots appear left-to-right from top to bottom.

Formula

Forward elimination: zeros below each pivot

Frequently Asked Questions

What is row echelon form?

A matrix is in row echelon form when all zero rows are at the bottom, each leading entry (pivot) is to the right of the pivot in the row above, and all entries below a pivot are zero.

What is the difference between REF and RREF?

REF zeros out only entries below pivots. RREF (reduced row echelon form) also zeros out entries above pivots and scales each pivot to 1.