I have this theorem in my notes but no proof and can't work out how to prove it (or find a proof via google):
Let T: V -> W be a linear transformation. Then T is onto iff Im (T) = W.
The Attempt at a Solution
I've only used this to prove other stuff.. so ideas on where to start proving this would be good. I understand the general idea that for T to be onto the image of T must contain the whole of W.. is that it?