Find the \(3 \times 3\) matrix that produces the described composite \(2\)D transformation below, using homogeneous coordinates.

Translate by \((-3,2)\), and then scale the \(X\)-coordinate by \(0.2\) and the \(Y-\)coordinate by \(1.2.\)

I have the answer key and don't need to send in an answer, so I'm not simply looking for the solution. I want to know how to solve it so I can solve similar problems.

Can anyone help me out at all?

I would like to be able to solve this kind of problem, but I don't understand the method of solving it.