Problem

Let V, W, and Z be vector spaces, and let T: V → W and U: W → Z be linear. (a) Prov...

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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Solutions For Problems in Chapter 2.3