Maths & numbers
Row reduction, rank & nullspace
Reduce a small matrix and inspect pivot columns, numerical rank and nullspace basis.
A clear answer. Here’s how.
Gauss–Jordan elimination uses partial row pivoting and a scale-aware numerical pivot threshold. Reports RREF, pivot columns, numerical rank and a basis for homogeneous solutions. Nullspace basis vectors appear as rows in the exported table. Up to 6 × 6; threshold is 10⁻¹⁰ × max(1, largest absolute entry) × max(rows, columns). Near-dependent data may be classified differently at another tolerance.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Matrix: one row per line
1, 2, 3 2, 4, 6
Example result
| Section | Row | C1 | C2 | C3 |
|---|---|---|---|---|
| RREF | 1 | 1 | 2 | 3 |
| RREF | 2 | 0 | 0 | 0 |
| Nullspace basis | 1 | -2 | 1 | 0 |
| Nullspace basis | 2 | -3 | 0 | 1 |
Numerical rank 1; pivot columns 1. Pivot tolerance = 10⁻¹⁰ × max(1, largest absolute entry) × max(rows, columns). Nullspace vectors are rows in the export.