Let V and W be vector spaces, let T : V--->W be linear, and let {w1, w2,...wk} be a linearly indepemdent subset R(t). Prove that if S={v1,v2,...vk} is chosen so that T(vi)=wi for i=1,2,.....k, then S is lenearly independent.

i've been trying to do that problem for ever.. dont know how to! plz help!