Now, , so
Now, , our job is to find x , y, and z.
Well, guess what? Plug in in for x, y, z, and see if they agree.
And that is the first half of your answer.
I'm also learning this stuff now in my class, and the matrix representation of a linear transformation is really a b to understand, I kept searching on the internet to find a good example, here is one if you want to see it.