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 (fraction) mode and Decimal mode?
Exact mode keeps every step as BigInt fractions so the RREF and solutions stay exact. Decimal mode uses floating point numbers rounded to the requested digits with partial pivoting for numerical stability.
How detailed are the operation logs for RREF and inverses?
Each row operation is recorded as swap, scale, or elimination along with the coefficients. For augmented matrices the log also notes that the same operation was applied to the augmented side, so you can replay the whole process.