Matrix Rank Calculator
Enter a matrix to compute its rank via Gaussian elimination (row reduction). Shows the number of rows and columns, full-rank check, and the reduced row echelon form (RREF).
Input
Enter one matrix row per line; separate entries with spaces or commas.
Result
Rank
2
Rows
3
Columns
3
Full rank
No
Reduced row echelon form (RREF)
Columns containing a pivot are shown in bold.
| 1 | 0 | -1 |
| 0 | 1 | 2 |
| 0 | 0 | 0 |
How it works
- Enter one matrix row per line; separate the entries in each row with spaces, tabs, or commas. Blank lines are ignored.
- The rank is found by reducing the matrix to reduced row echelon form (RREF) with Gauss-Jordan elimination and counting the pivots (non-zero rows).
- To absorb floating-point rounding, values with absolute value below about 1e-9 are treated as zero.
- A matrix has full rank when its rank equals the smaller of the row and column counts, min(rows, cols).
- Row rank always equals column rank, so row reduction alone determines the rank.
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Matrix Rank Calculator