Let V, W, and Z be vector spaces, and let T: V → W and U: W → Z be linear.
(a) Prove that if UT is one-to-one, then T is one-to-one. Must U also be one-to-one?
(b) Prove that if UT is onto, then U is onto. Must T also be onto?
(c) Prove that if U and T are one-to-one and onto, then UT is also.
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