If it were a bijection then you could use the fact that F is linear, i.e.
.
Not sure if this is really that helpful though.
Hi! I've been trying to figure this out, but I'm not sure how I'd prove it..
Let V, W be two vector spaces, and F: V-->W a linear map. Let w_1, ..., w_n be elements of W which are linearly independent, and let v_1, ..., v_n be elements of V such that F(v_i)=w_i for i = 1, ..., n. Show that v_1, ..., v_n are linearly independent.
Help please! Thank you
Yeah, that was my point HallsofIvy. The problem is that a linear transformation that maps more than one vector to the zero vector. For this to be true we must require the only vector mapped to the zero vector be the zero vector, otherwise the proof I wrote up doesn't work.