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Math Help - Matrix help

  1. #1
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    Matrix help

    A = \begin{bmatrix} 1 & 1 & 0 \\0 & 2 & 1 \\-4 & -11 & -4 \end{bmatrix}

    find the smallest value of n > 0 such that

    I need help on this question, I am suppose to solve it using matlab, however, I dont even know how to solve this on paper, let alone matlab, any suggestions or help appreciated.

    I have tried to to it like this

     A^{-1}A^{n} =IA^{-1}

     n = IA^{-1}
    to get n, and matlab gives me,

    \begin{bmatrix} -3 & -4 & -1 \\4 & 4 & 1 \\-8 & -7 & -2 \end{bmatrix}

    so is n = 1? Is this correct?

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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Matrix help

    Quote Originally Posted by Tweety View Post
    A = \begin{bmatrix} 1 & 1 & 0 \\0 & 2 & 1 \\-4 & -11 & -4 \end{bmatrix}

    find the smallest value of n > 0 such that

    I need help on this question, I am suppose to solve it using matlab, however, I dont even know how to solve this on paper, let alone matlab, any suggestions or help appreciated.

    I have tried to to it like this

     A^{-1}A^{n} =IA^{-1}

     n = IA^{-1}
    to get n, and matlab gives me,

    \begin{bmatrix} -3 & -4 & -1 \\4 & 4 & 1 \\-8 & -7 & -2 \end{bmatrix}

    so is n = 1? Is this correct?

    Hi Tweety!

    If you fill in n=1, you'll get A^n = A^1 = A.
    That does not look like the identity matrix.
    So no, it is not n=1.

    If you're using matlab you might simply iterate over n, calculate A^n and see if it matches the identity matrix.

    Using a little math would be to calculate the eigenvalues.
    If any of them has an absolute value that deviates from 1, it is not possible.
    Then you need to find the lowest integer power that will turn all eigenvalues into 1.
    If there is one, that is your prime candidate.
    You will still have to verify if it fits.
    Thanks from Tweety
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  3. #3
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    Re: Matrix help

    Thank you, but still slightly confused...

    I defined my matrix in matlab, and calculated a^n , for different values of n, 1,2,3 etc... but get no where near the idenity matrix
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  4. #4
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    Re: Matrix help

    Actually I just tried a^4 and got the indenity matrix, thank you sooo much
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