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Math Help - Power of a Matrix

  1. #1
    Junior Member shannu82's Avatar
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    Exclamation Power of a Matrix

    A = {[2 1 2 ] [2 1 2 ] [2 1 2 ]}^8
    Compute the power matrix using the PDP^-1
    I got the eigen values to be 1, 2.
    i am having difficulty forming the vector and therefore continuing the question. Could anyone explain this?
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Quote Originally Posted by shannu82 View Post
    A = {[2 1 2 ] [2 1 2 ] [2 1 2 ]}^8
    Compute the power matrix using the PDP^-1
    I got the eigen values to be 1, 2.
    i am having difficulty forming the vector and therefore continuing the question. Could anyone explain this?
    Is that meant to mean that the three rows of A are all equal to 1 2 1? If so, the eigenvalues are 0 and 5, not 1 and 2. Please supply a correct version of the problem.
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  3. #3
    Junior Member shannu82's Avatar
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    Quote Originally Posted by Opalg View Post
    Is that meant to mean that the three rows of A are all equal to 1 2 1? If so, the eigenvalues are 0 and 5, not 1 and 2. Please supply a correct version of the problem.
    um the question actually looks like
    [212]
    [212]
    [212]

    That whole matrix to the power of 8.
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  4. #4
    MHF Contributor
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    Quote Originally Posted by shannu82 View Post
    um the question actually looks like
    [212]
    [212]
    [212]

    That whole matrix to the power of 8.
    Have you tried multiplying the matrix by itself to see what its square looks like? If so, did you notice that the square is exactly 5 times the original matrix? So what would happen if you squared the result again? And again?
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