Combine Scaling and Translation Matrices

Hello all,

I am revising for a maths resit paper taking place next week and could really do with some help regarding this past paper question.

**Derive a single matrix to undertake the following collective 2D transformations. A Scaling by a factor of 2 in both X and Y directions followed by a translation by 2 in the X direction and 3 in the Y direction.**

Any advice regarding this would be much appreciated as I am pulling out what's left of my hair trying to figure it out.

I *think* I need to do this first:

Scaling by 2 in both X and Y directions =

X' = Sx * X Y' = Sy * Y

Translation by 2 in X and 3 in Y directions would follow as =

X' = X + tx Y' = Y + ty

Scaling Matrix would be:

|X'| |2 0| |X|

|Y'|=|0 2|* |Y|

Translation Matrix would be:

|X'| |2 0| |X|

|Y'|=|0 3|* |Y|

And now to combine the two matrices in some way?

Once again, ANY help would be great.

Cheers (Happy)