If T1 :Rn→Rm and T2 :Rm→Rk are linear transformations, and if T1 is not onto, then neither is T2 ◦ T1.
I think it's False b/c if T2 (ran(T1)) = Rk then T2◦T1 is onto? Is there a more generic way for me to say that? THANKS!
For arbitrary (not necessarily linear) functions, if T2 ◦ T1 is onto than so is T2, and if T2 ◦ T1 is an injection, then so is T1. One should be skeptical about stronger claims.