# Linear Algebra help

• Jul 13th 2008, 11:21 AM
JCIR
Linear 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, 11:57 AM
JaneBennet
Part (a) is straightforward (use the definition of 1–1 function).

Part (b): No, $U$ only has to be 1–1 on the subspace $T(W)$.