Matrix Input
Example data table
Sample augmented matrix (3×4). Last column is constants.
| c1 | c2 | c3 | b |
|---|---|---|---|
| 1 | 2 | -1 | 3 |
| 2 | 4 | 1 | 7 |
| -1 | -2 | 5 | -1 |
Click “Fill Example” to load this matrix instantly.
Formula used
Reduced row echelon form is computed using Gauss–Jordan elimination. The algorithm applies three elementary row operations:
- Rᵢ ↔ Rⱼ (swap two rows)
- Rᵢ ← k·Rᵢ (scale a row by nonzero k)
- Rᵢ ← Rᵢ − k·Rⱼ (eliminate with a pivot row)
Each pivot is normalized to 1, then all other entries in that column become 0.
How to use this calculator
- Choose your matrix rows and columns, then build the grid.
- Enter values in each cell; fractions like -2/5 work.
- Optionally enable the step log for detailed row operations.
- If solving a system, mark the last column as constants.
- Press Submit to display the RREF above this form.
- Use Download buttons to export the computed matrix.