Matrix Calculator (with steps)
RREF / Solve Ax=b / Inverse / Determinant — rank, null space, row/column spaces
Result
How it's calculated
Teacher Notes
Exact mode uses BigInt fractions for reproducible steps. Decimal mode uses partial pivoting for stability. Row operations follow determinant rules: swap → sign flip; scale by k → multiply det by k; add → determinant unchanged.
FAQ
What is the difference between Exact and Decimal modes?
Exact keeps every intermediate value as a fraction, which is perfect for proofs or grading. Decimal works with rounded floating point numbers so you can follow the same elimination steps that appear on a calculator or in engineering work.
How detailed are the RREF and inverse step logs?
Every row swap, scaling, and elimination is recorded together with the coefficient that was used. For augmented matrices the log indicates that the right-hand side was updated in the same way, so you can reconstruct each step precisely.