Row Echelon Form Calculator
Transform a matrix into its row echelon form (REF) or reduced row echelon form (RREF).
Select Matrix Size
Select Form Type
Row Echelon Form (REF)
A matrix is in row echelon form if:
- All zero rows are at the bottom
- Leading coefficient (pivot) is to the right of the pivot above it
- All entries below a pivot are zero
Reduced Row Echelon Form (RREF)
A matrix is in reduced row echelon form if it is in REF and:
- All pivots are 1
- All entries above pivots are zero
- Each pivot is the only non-zero entry in its column
Applications:
- Solving systems of linear equations
- Finding matrix rank
- Computing determinants
- Finding null space
- Matrix inversion
Properties:
- REF is not unique
- RREF is unique
- Preserves solution space
- Reveals linear dependencies