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Math Help - How to find matrix A power 5 using caley hamilton theorem?

  1. #1
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    How to find matrix A power 5 using caley hamilton theorem?

    Hi. I`m new here, so hope I can get some help. Did a search but didnt find anything on it.
    Anybody can help me find Matrix A power 5 using Caley Hamilton theorem (no other option allowed here).
    A=[1 1 -1
    1 1 1
    1 1 1]
    Thanks!
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  2. #2
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    Quote Originally Posted by molokomesto650 View Post
    Hi. I`m new here, so hope I can get some help. Did a search but didnt find anything on it.
    Anybody can help me find Matrix A power 5 using Caley Hamilton theorem (no other option allowed here).
    A=[1 1 -1
    1 1 1
    1 1 1]
    Thanks!
    The first thing you need to do is get the characteristic equation. Please post those calculations.
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  3. #3
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    that would be (unless mistake)
    - λ^3+3 λ^2-2 λ
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  4. #4
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    the characteristic equation is p(\lambda)=\lambda^3-3\lambda^2+2\lambda

    so

    A^3-3A^2+2A=0

    and

    A^5=3A^4-2A^3
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  5. #5
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    thanks to both of you. Very helpful.
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