MST10030 notes wiki

If we perform one of the following operations on a system of linear equations:

1. list the equations in a different order; or
2. multiply one of the equations by a non-zero real number; or
3. replace equation $j$ by “equation $j$ ${}+{}$ $c\times {}$ (equation $i$)”, where $c$ is a non-zero real number and $i\ne j$,

then the new system will have exactly the same solutions as the original system. These are called elementary operations on the linear system.