Overview
LU Decomposition factors a matrix \( A \) into a lower triangular matrix \( L \) and an upper triangular matrix \( U \) such that \( A = LU \). This page covers the manual procedure using forward and backward substitution as well as a computer-based approach.
Manual Steps
- Express \( A \) as \( LU \) with \( L \) (lower triangular with 1’s on the diagonal) and \( U \) (upper triangular).
- Solve \( Ly = b \) by forward substitution.
- Solve \( Ux = y \) by backward substitution.