# Gaussian elimination

### From Glossary

A method to solve that performs elementary row operations on to
annihilate successive elements of in order to reduce to an
upper triangular matrix, . On paper, the same operations are
applied to , then the solution is obtained by solving the
resulting upper triangular system. In a computer, the product of
the matrices effecting the elementary row operations is a lower
triangular matrix, , with unit diagonal. Once this phase is
completed, the system becomes . This is then solved in
two steps: forward substitution solves ;
then backward substitution solves . (Of course, computer implementations
vary.)