We can solve a system of linear equations written in matrix form by performing 'elementary row operations' on the augmented matrix.

There are three types of elementary row operations.
1. Interchanging two rows.

2. Rep;ace any row by a non zero multiple of itself.

3. Replace any row by itself plus or minus a non zero multiple of another row.

The rows represent equations, so each of these operations is an operation on the equations. We aim to manipulating the matrix into upper triangular form. The solution can be obtained by back substitution.