## UCT MAM1000 lecture notes part 50 – linear algebra part iii

**Gauss reduction**

So far we have seen that we have a way to translate a system of linear equations into a matrix. We can manipulate the matrix in ways which correspond to operations on the equations which keep the important information in the system of equations the same (ie. the solution of the equations before and after the operations is the same). We have seen a couple of examples of when we can read off the solution from the matrix having performed the operations. So far the order with which we perform the operations feels a bit arbitrary, although we know that we would like to get the matrix into reduced row echelon form. There is however a very systematic way of going about this, and the term for the process is called *Gauss Reduction***.**

Here is a detailed view of what Gauss Reduction will give us:

**Gauss Reduction:
**

To solve a system of linear equations:

1) First find the augmented coefficient matrix of the system of equations.…