http://img231.imageshack.us/img231/4...enshot1png.jpg

(link to the problems)

If anyone could explain how to do this, that would be amazing. I know that to be linear, a transform has to satisfy T(u + v) = T(u) + T(v) and T(ku) = kT(u), but i'm not sure how to apply it in all of these situations.

Thanks in advance!