🔗 Linear System Solver

Linear System Solver Ax = b

Solve systems of linear equations. Detects unique, infinite, or no solution. Shows augmented matrix RREF and back-substitution with full steps.

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System of Linear Equations Ax = b

Enter coefficient matrix A and constants b

✓ Consistency Check✓ Step-by-Step✓ Free⚡ Loading SymPy Engine…

Equations (rows)

Variables (cols)

Coefficient Matrix A

Constants b

Quick Examples

Types of Solutions

Unique solution: rank(A) = rank([A|b]) = n. One exact solution vector x.
Infinite solutions: rank(A) = rank([A|b]) < n. Free variables exist.
No solution: rank(A) < rank([A|b]). System is inconsistent.

Solution Method

This solver uses augmented matrix RREF (Gauss-Jordan elimination), which systematically reduces [A|b] to [I|x] for unique solutions or identifies pivot/free variables for other cases.