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
So you have
$\displaystyle \left(\begin{array}{c}x' \\ y'\end{array}\right)= \left(\begin{array}{cc}cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta)\end{array}\right)\left(\begin{array}{c } x \\ y\end{array}\right)$
The augmented matrix is
$\displaystyle \left(\begin{array}{ccc}cos(\theta) & -sin(\theta) & x' \\ sin(\theta) & cos(\theta) & y'\end{array}\right)$
Do you know how to row-reduce that?
This is, by the way, the matrix corresponding to rotation through angle [itex]\theta[/itex]. It has an obvious, easy, inverse that you can use to check your answer.