I have this problem from my Graphics course. Given this transformation matrix:
$\begin{pmatrix} -2 &-1& 2\\ -2 &1& -1\\ 0 &0& 1\\ \end{pmatrix}$
I need to extract translation, rotation and scale matrices. I've also have the answer (which is $TRS$): $T=\begin{pmatrix} 1&0&2\\ 0&1&-1\\ 0&0&1\end{pmatrix}\\ R=\begin{pmatrix} 1/\sqrt2 & -1/\sqrt2 &0 \\ 1/\sqrt2 & 1/\sqrt2 &0 \\ 0&0&1 \end{pmatrix}\\ S=\begin{pmatrix} -2/\sqrt2 & 0 & 0 \\ 0 & \sqrt2 & 0 \\ 0& 0& 1 \end{pmatrix} % 1 0 2 1/sqrt(2) -1/sqrt(2) 0 -2/sqrt(2) 0 0 %T = 0 1 -1 R = /1/sqrt(2) 1/sqrt(2) 0 S = 0 sqrt(2) 0 % 0 0 1 0 0 1 0 0 1 $
I just have no idea (except for the Translation matrix) how I would get to this solution.