## Transformations proof

Let S:V --> W and T:U --> V be linear transformations. Prove that
a) if S(T) is one-to-one, then T is one-to-one
b) if S(T) is onto, then S is onto

This makes intuitive sense to me, since S(T) maps U to W, but I can't figure out how to go about proving this.

I would appreciate any help at all. Thank you.

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
 Recognitions: Gold Member Homework Help Science Advisor a) Suppose that T is not one-to-one, but S(T) is one-to one. Since there exist at least u1, u2 in U, so that T[u1]=T[u2]=v1, then we would have S(T[u1])=S[v1]=S(T[u2])=w1, i.e, we have a contradiction, since S(T) is premised to be one-to-one.
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