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.
What should I do first on this page?
Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.
Why does this page differ from another tool?
Different pages often use different defaults, units, rounding rules, or assumptions. Align those settings before comparing outputs. If differences remain, compare each intermediate step rather than only the final number.
How reliable are the displayed values?
Values are computed in the browser and rounded for display. They are good for planning and educational checks, but for regulated or high-stakes decisions you should validate assumptions with official guidance or professional review.
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.