How it works
Apply Gaussian elimination with partial pivoting to an n×(n+1) augmented matrix. Normalize each pivot and eliminate its column from other rows.
Input definitions
- Augmented matrix: coefficients then right-hand side, no header
- Plain text; maximum 200,000 characters.
A worked example
- Augmented matrix: coefficients then right-hand side, no header
- 2,1,5 1,-1,1
Assumptions & limits
Square systems with a unique numerically stable solution, up to 10 variables. Coefficients within ±10¹²; no symbolic or least-squares solution.
Sources & review
Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.
Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.
Common questions
Why does the solver reject a system instead of returning numbers?
A singular system may have no unique solution. Very small pivots relative to the coefficient scale indicate numerical instability, so the tool rejects the case rather than presenting a misleading unique answer.
How does Solve a linear equation system work?
Apply Gaussian elimination with partial pivoting to an n×(n+1) augmented matrix. Normalize each pivot and eliminate its column from other rows.
What are the limits of Solve a linear equation system?
Square systems with a unique numerically stable solution, up to 10 variables. Coefficients within ±10¹²; no symbolic or least-squares solution.