Exact rational linear algebra
Linear System Solver
Solve systems of linear equations using an augmented matrix and exact row reduction.
Matrix A
3 x 3
Matrix B
3 x 3
Basic
Square Matrix
Row Reduction
How it works
- Matrix A is treated as the coefficient matrix and Matrix B as the right-hand-side column vector.
- The calculator row-reduces [A | b] and checks pivot structure carefully.
- It distinguishes unique, inconsistent, and infinite-solution systems.
Common mistakes
- Using a Matrix B that is not a column vector.
- Giving A and B different row counts.
- Assuming every square system has a unique solution.
FAQ
What if there are infinitely many solutions?
The calculator reports that free variables remain after reduction.
Can I see the elimination steps?
Yes. Step mode shows the row operations used in the solve process.