I'm in a little slump with this question. I have a general idea, but I don't know exactly which theorem to pair them up with because I think that it may be too simple. Here is the question:
For part (a) I was thinking that if T is a linear transformation, and if T is one-to-one, then it has the trivial solution T(x) = 0. Doesn't that imply linear independence already, or am I missing a step?
For part (b) I was thinking that X spans V if then it is a subspace of V, but I don't know how it works with span W.
Any tips on these problems?
The usual route is rewrite $\sum_i c_i T(x_i) = 0$.
For both of those. Show us exactly where you're getting stuck and you might unstick yourself.