Home
Categories
Linear Algebra Calculus Differential Equations Number Theory Statistics Optimization About Contact

Linear Systems Solver

Solve Ax = b using Gaussian elimination.

System (augmented matrix [A|b])
Solution

Enter the augmented matrix.

Technical Description & Theory

What is Linear Systems Solver and Why it Matters?

Solving A x = b is the most frequent task in applied mathematics, supporting analyses from circuit theory to structural mechanics.

Mathematical Formula and Theory

Gaussian elimination with partial pivoting transforms [A|b] into upper-triangular form, followed by back-substitution. Complexity is O(n³).

How to Use This Calculator - Step by Step

  • Select system size n.
  • Enter coefficient matrix and right-hand side b.
  • Click Solve System.

Solved Example with Full Calculation

Solve [[2,1,−1],[−3,−1,2],[−2,1,2]] [x,y,z]T = [8,−11,−3]T. Solution: x=2, y=3, z=−1.