Linear Algebra Solver
Enter matrix A and, optionally, the right-hand side b. The tool works with exact rational numbers: it computes RREF, det(A), inverse matrices, and Ax=b systems with row-operation steps.
Input
Separate rows with line breaks or semicolons, and entries with spaces or commas. Integers, decimals, and fractions such as 7/12 are supported.
Result
Choose an action to see the computation.
Row operations
No row operations were needed.
Why this is useful
- Check linear algebra homework without losing exactness to floating-point rounding.
- See the answer and the elementary row operations that produced it.
- Quickly distinguish a unique solution, an inconsistent system, and a family of parametric solutions.
- Prepare clean fractional answers for notes, reports, or manual-solution checks.
Quick reference
RREF reveals pivot variables, rank, and free parameters. Determinants and inverse matrices are computed through the same row operations. All calculations run locally in the browser.
How to use it
- Enter matrix A: one row per line or separated by semicolons, elements separated by spaces or commas. Integers, decimals and fractions like 7/12 are accepted.
- To solve Ax = b, add the right-hand side vector b.
- Press Solve. The tool reduces the matrix to echelon form and RREF, computes the rank, determinant and inverse (for square matrices), and finds the solution of the system or shows that there is none or infinitely many.
- Expand the steps to see every elementary row operation — handy for checking homework.
When it helps
- Checking homework: compare your working with a step-by-step derivation, not just the final answer.
- Systems of equations: quickly learn whether a system is consistent and get the general solution with free variables.
- Engineering calculations: find an inverse or determinant of a small matrix without Python or MATLAB.
Frequently asked questions
Why are answers fractions rather than decimals?
Computation uses exact rational arithmetic, so 1/3 stays 1/3 instead of 0.3333. Rounding errors do not accumulate and the answer matches a textbook.
What does “infinitely many solutions” mean?
The rank is smaller than the number of unknowns: some variables are free and the solution is written in terms of them as parameters. The RREF shows which ones.
How large can the matrix be?
About 10×10 in practice: beyond that the step-by-step output becomes very long, although the calculation itself is fast.