# Proof of composite linear transformations

1. Mar 9, 2005

### Flyboy27

Prove that if $$T:R^{m} \rightarrow R^{n}$$ and $$U:R^{n} \rightarrow R^{p}$$ are linear transformations that are both onto, then $$UT:R^{n} \rightarrow R^{p}$$ is also onto.

Can anyone point me in the right direction? Is there a theorem that I can pull out of the def'n of onto that I can begin this proof?

2. Mar 9, 2005

### mathwonk

this is trivial, direct from definition of onto.