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

  1. Jun 12, 2007 #1


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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
    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?
  2. jcsd
  3. Jun 12, 2007 #2


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    Homework Helper

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