# Gauss-Jordan elimination

### From Glossary

A method to solve that performs elementary row and column operations on to annihilate successive elements of in order to reduce to an identity matrix. On paper, the same operations are applied to , then the solution is obtained by solving the resulting identity system. In a computer, the matrices effecting the elementary operations are saved as elementary matrices, say for the i-th operation. Then, the system is equivalent to , and forward transformation is applied to solve for . This is what is done in the (revised) simplex method, and each iteration is a pivot operation.