Exact rational linear algebra
Rank Calculator
Compute matrix rank by reducing to RREF and counting the nonzero pivot rows.
Matrix A
3 x 3
Matrix B
3 x 3
Basic
Square Matrix
Row Reduction
How it works
- The calculator finds the RREF of your matrix with exact arithmetic.
- It counts how many rows remain nonzero after reduction.
- Rank works for square and rectangular matrices.
Common mistakes
- Confusing rank with determinant.
- Expecting singular square matrices to have full rank.
- Overlooking dependent rows.
FAQ
Can rectangular matrices have full rank?
Yes. Full rank depends on the smaller matrix dimension.
Why does rank use RREF?
RREF makes pivot rows easy to identify exactly.