Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of composite linear transformations

  1. Mar 9, 2005 #1
    Prove that if [tex]T:R^{m} \rightarrow R^{n}[/tex] and [tex]U:R^{n} \rightarrow R^{p}[/tex] are linear transformations that are both onto, then [tex]UT:R^{n} \rightarrow R^{p}[/tex] 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. jcsd
  3. Mar 9, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    this is trivial, direct from definition of onto.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Proof composite linear Date
A Is the proof of these results correct? Jan 29, 2018
I Doubt about proof on self-adjoint operators. Nov 11, 2017
Riemann proof effect on factoring composites Jun 13, 2009
Proof of composites Oct 2, 2008