Let V, W, and Z be vectors spaces, and let T: V --> W and U: W --> Z be linear. Prove that if UT is 1-1, then T is 1-1. b) does U have to be 1-1?
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Part (a) is straightforward (use the definition of 1–1 function). Part (b): No, $\displaystyle U$ only has to be 1–1 on the subspace $\displaystyle T(W)$.
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