Your scaling matrix looks good, but your "translation" matrix is actually still a scaling matrix. To translate by
, simply add the vectors:
Alright, so given some (x,y) pair, you're going to scale x by 2 and then translate by 2. So
So we know our solution should look something like this, but we don't have the answer in matrix form.
You're right that we need to combine the two operations--to accomplish this, just do one after the other. First scale, then translate.
And look, this is the same as the equations for and given above. Hopefully this helps.