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Math Help - Prove or disprove question

  1. #1
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    Prove or disprove question

    Prove or dispove

    T:R^n \rightarrow R^n is a linear transformation

    if for every u \in R^n and for every v \in KerT,
    T(u) \cdot v=0

    then KerT = (ImT)^{\perp}

    Attempt:

    even though these questions are always false, sadly I chose True and gave an explanation why.

    If this is false can someone please explain why and give an example.
    (even if it's true can you explain why)

    Thanks!
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by jayshizwiz View Post
    Prove or dispove

    T:R^n \rightarrow R^n is a linear transformation

    if for every u \in R^n and for every v \in KerT,
    T(u) \cdot v=0

    then KerT = (ImT)^{\perp}

    Attempt:

    even though these questions are always false, sadly I chose True and gave an explanation why.

    If this is false can someone please explain why and give an example.
    (even if it's true can you explain why)

    Thanks!
    Would it maybe not be more helpful to you, if you wrote out the reason why you believe it to be true?
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  3. #3
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    if T(u) \cdot v = 0

    that must mean

    a) KerT=\bar{0} and ImT = R^n
    or
    b) KerT=R^n and ImT=\bar{0}

    and in both those cases kerT= (ImT)^\perp

    Is there any error in my reasoning?

    Thanks!
    Last edited by jayshizwiz; November 7th 2010 at 12:41 PM.
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  4. #4
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    Does anybody have an idea? Is the question clear?
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