Math Help - gauss jordan elimination

1. gauss jordan elimination

Hello i need help to solve this:

Use gauss jordan elimination to solve for x' and y' in terms of x and y

the matrix is:

cos(theta) -sin(theta) x
sin(theta) cos(theta) y

thank you

2. So you have
$\left(\begin{array}{c}x' \\ y'\end{array}\right)= \left(\begin{array}{cc}cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta)\end{array}\right)\left(\begin{array}{c } x \\ y\end{array}\right)$

The augmented matrix is
$\left(\begin{array}{ccc}cos(\theta) & -sin(\theta) & x' \\ sin(\theta) & cos(\theta) & y'\end{array}\right)$
Do you know how to row-reduce that?

This is, by the way, the matrix corresponding to rotation through angle $\theta$. It has an obvious, easy, inverse that you can use to check your answer.