Gaussian Elimination

Numerical Analysis · Axiom Academy

Transform any system into triangular form, then solve by back substitution Three operations that don't change the solution set: Eliminate entries below each pivot to create zeros: With upper triangular form, solve from bottom to top: Watch the full algorithm on a 3×3 system: Forward elimination: O(n³/3) Back substitution: O(n²/2) • Exact (up to round-off) • Works for any n×n system • Needs non-zero pivots

This is the written version of the interactive lesson above. See the full Numerical Analysis course.