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Math Help - Image and kernal

  1. #1
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    Image and kernal

    Image and kernal-untitled.jpg



    Hi could some please just help me to find the image and kernal of the linear transformation and i should be able to prove the rest.


    thanks
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  2. #2
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    Do you understand that you do not need to, and, indeed, are not expected to actually find the image and kernel in order to do this? You are told that T^2(v)= T(T(v))= 0 for every v in the vector space. There are an infinite number of functions, T, that will do that and they have different images and kernels. In order to prove that, for such a function, Im(T)\subseteq Ker(T) you just need to know the definitions of "image" and "kernel".
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  3. #3
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    Hi, i just tryed the proof,

    Know T(v)=Im(T).
    So
    T^2(v)= T(T(v))=T(Im(T))=0

    Thus image is a subset of the kernal
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  4. #4
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    Hi, i just tryed the proof,

    Know T(v)=Im(T) .

    So

    T^2(v)= T(T(v))=T(Im(T))=0

    Thus image is a subset of the kernal
    Last edited by nerdo; October 31st 2010 at 07:36 AM.
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  5. #5
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    is what i wrote above correct?
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