What is Row Echelon Form?
Row Echelon Form (REF) is a fundamental matrix form in linear algebra characterized by:
- All zero rows at the bottom
- Leading coefficient (pivot) of a non-zero row is to the right of the pivot above
- All entries below pivots are zero
Key Applications
- Solving systems of linear equations
- Matrix rank calculation
- Basis determination for vector spaces
- Matrix inversion
How the Calculator Works
- Input your matrix using integer or decimal values
- Adjust matrix dimensions as needed
- Click calculate to perform Gaussian elimination
- View results and step-by-step operations
Gaussian Elimination Steps
1. Start with leftmost non-zero column (pivot column)
2. Select non-zero pivot element
3. Swap rows to bring pivot to top
4. Normalize pivot row
5. Eliminate entries below pivot
6. Repeat for next pivot to the right