Let S V W and T U V be linear transformations (a) Prove that if S and T are both one to one, so is S T (b) Prove that if S and T are both onto, so is S T

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

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

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a Suppose that S T u 0 Then S T u S Tu 0 Since S is onetoone we mus... View full answer

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