📋 Reduced Row Echelon Form Calculator
Convert matrix to RREF using Gaussian elimination
How to Use This Calculator
1
Set Dimensions
Choose rows and columns.
2
Enter Matrix
Input all matrix elements.
3
Get RREF
Compute reduced row echelon form and rank.
Formula
RREF: Leading 1 in each row, zeros above/below pivots
RREF Properties:
- Leading 1 in each nonzero row
- Zeros above and below each leading 1
- Leading 1s move right as you go down rows
- Zero rows at bottom
- Unique form for any matrix
About Reduced Row Echelon Form
Reduced Row Echelon Form (RREF) is a canonical form of matrices produced by Gaussian elimination. It's unique and reveals rank, null space, and solution structure of linear systems.
Applications
- Solve linear systems
- Find rank and null space
- Determine linear independence
- Find inverse matrices
Frequently Asked Questions
Why is RREF unique?
Every matrix has exactly one RREF. The specific sequence of row operations doesn't matter—the final result is always the same.
What's the difference between REF and RREF?
REF (Row Echelon Form) has leading 1s and zeros below pivots. RREF additionally has zeros above pivots.