Let V and W be vector spaces, let T: V --> W be linear, and let {w1, w2,...,wk} be a linearly independant subset of R(T). Prove that if S = {v1,v2,...,vk} is chosen so that T(vi) = wi for i = 1, 2 ,...,k, then S is linearly independent.
My prof had mention about taking the image of both sides, however I still don't see where to start