Gaussian Elimination

Updated 01 Oct 2026

•
What it is
- •
  uses elementary row operations to transform a linear system into upper-triangular form, followed by back substitution
•
Pivoting
- •
  partial pivoting selects a largest-magnitude available entry in the current column and swaps rows
- •
  apply each row operation to the right-hand side as well as the coefficient matrix
•
Cautions
- •
  a zero pivot may require a row exchange; it does not by itself prove that the original system has no solution
- •
  pivoting helps avoid unstable divisions but cannot cure an ill-conditioned underlying problem
•
Related
- •
  LU Decomposition
- •
  Condition Number

Linked references 4