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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


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    this is trivial, direct from definition of onto.
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