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Prove a given transformation exists or not: T: R^4 -> R^5

  1. Jun 12, 2007 #1

    daniel_i_l

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    Gold Member

    1. The problem statement, all variables and given/known data
    Prove if the following transformation exists or not: T: R^4 -> R^5
    where: KerT=Sp{(0,1,1,0),(1,1,0,0)} , ImT=Sp{2,3,4,0,0),(1,1,0,0,0),(0,1,1,0,0)}


    2. Relevant equations
    T:V->W
    dimImT + dimKerT = dimV


    3. The attempt at a solution
    I think that the answer is no because dimKerT=2 , dimImT=3 but 2+3 =/= 4.
    Is that right? Am I missing something?
    Thanks.
     
  2. jcsd
  3. Jun 12, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    Yes, it's right. No, you aren't missing anything.
     
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