Transform a matrix into Row Echelon Form (REF) using Gaussian elimination.
Input 3x3 Matrix
Resulting REF
Forward Elimination Complete
REF Result
Matrix with zeros below each leading entry.
7.00
8.00
9.00
0
0.86
1.71
0
0
0
TriangularUpper
Pivots2
About this calculator
Quick Reference
PhaseForward Elimination
ZerosBelow Pivots
FormUpper Triangular
What is Row Echelon Form?
Row Echelon Form (REF) is a matrix form resulting from the first phase of Gaussian elimination. A matrix is in REF if all zero rows are at the bottom, and the leading entry of each non-zero row is to the right of the leading entry above it. Unlike RREF, entries above the leading ones do not have to be zero.
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Pro Tips
Staircase Pattern: Look for the 'staircase' of zeros in the bottom-left of the matrix.
Leading Entries: While often simplified to 1, any non-zero value can be a leading entry in generic REF.
Gaussian Elimination: Stop after you have zeros below all your pivots to reach REF.
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Fun Facts
"REF is used during 'forward elimination' in numerical linear algebra."
"A square matrix in REF is also an upper triangular matrix."
