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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- Jul 13th 2008, 10:21 AMJCIRLinear Algebra help
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? - Jul 13th 2008, 10:57 AMJaneBennet
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 $\displaystyle T(W)$.