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Math Help - dimention of kernel

  1. #1
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    dimention of kernel

    A is a 2X2 matrices.T is a transformation from M_{2X2}->M_{2X2}

    T differs zero. T is not isomorphism
    prove that dim ImT=dim KerT=2

    if T differs zero then its representative matrices A differs zero too.
    because T is not isomorphism then its singular so we have only one row
    of seros in A.

    so rank(A)=1 and null(A)=1
    so there is only one k 2X2 matrices which sends for which T(k)=0

    the solution in my book says that this k matrices is a tranposed
    vector (a,b)
    ??

    why??
    our result has to be 2x2 matrices
    whith
    transposed (a,b) we cant get 2x2 matrices


    ?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: dimention of kernel

    Quote Originally Posted by transgalactic View Post
    A is a 2X2 matrices. T is a transformation from M_{2X2}->M_{2X2} T differs zero. T is not isomorphism prove that dim ImT=dim KerT=2
    This is nonsense. What has to do A in respect to T ?
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  3. #3
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    Re: dimention of kernel

    if T maps a 2x2 matrix to a 2x2 matrix, then a representative matrix for T is 4x4. it is not clear from your question what "A" is.
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