Question: Let S: V W and T: U V be linear transformations. (a) Prove that if S T is one-to-one, so is T.

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

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a Suppose that Tu 0 Then since S0 0 we have S Tu S Tu S0 0 But S T is onetoone so we must have ... View full answer

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