Matrix Calculator (with steps)
RREF / Solve Ax=b / Inverse / Determinant — rank, null space, row/column spaces
Results
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.
When should I choose RREF versus Solve Ax=b?
Use RREF to study pivots, rank, and row-reduced form. Use Solve Ax=b when you have a coefficient matrix and right-hand side and want the solution set directly.
Why can an inverse or determinant fail?
Inverse requires a square nonsingular matrix, and determinant is defined for square matrices. If the matrix is singular, the inverse does not exist and the determinant is zero.
Should I use Exact or Decimal mode?
Use Exact mode for classroom answers, fractions, and reproducible row logs. Use Decimal mode for larger numeric systems where partial pivoting and rounded output are acceptable.
How to use Matrix Calculator — RREF / Solve Ax=b / Inverse / Determinant (with steps) effectively
What this calculator does
Use this page when you want matrix operations, exact fractions, and step logs in one place. Open Graphing Calculator for function plots, Algebra Simplifier for symbolic term work, and Vector Calculator when the problem is geometric vectors rather than row operations.
Input meaning and unit policy
Choose the matrix size and operation first, then paste or type values. Use Exact mode when you need reproducible fractions and Decimal mode when you care more about numerical stability on larger systems.
Use-case sequence
A practical sequence is: build the matrix, compute once, inspect the result block, then read the step log only if you need to explain the transformation or debug one row operation.
Common mistakes to avoid
Avoid mixing incompatible dimensions, comparing rounded decimal output with exact fractions, or copying a result before you confirm the chosen operation matches the matrix shape.
Interpretation guidance
Check the final matrix and the row-operation log together. If the result looks surprising, verify pivots and dimensions before assuming the algebra is wrong.