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Math Help - matrix eigenvalues **URGENT**

  1. #1
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    Exclamation matrix eigenvalues **URGENT**

    matrix is:

    0,0,1
    1,0,0
    0,1,0

    Find eigenvalues of matrix.

    Really stuck on how to do this as I work it out using the only method I know and get (0-λ ) (λ^2) + (λ ). Obviously a solution is 1 but I need to find two more??

    Thanks.
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  2. #2
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    Quote Originally Posted by geo3 View Post
    matrix is:

    0,0,1
    1,0,0
    0,1,0

    Find eigenvalues of matrix.

    Really stuck on how to do this as I work it out using the only method I know and get (0-λ ) (λ^2) + (λ ).
    no, this is wrong

    you get 1-t^3 and therefor one eigenvalue is +1


    Quote Originally Posted by geo3 View Post
    Obviously a solution is 1 but I need to find two more??
    No, you do not.
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  3. #3
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    how did you calculate 1-t^3??
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  4. #4
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    Quote Originally Posted by Rapha View Post

    you get 1-t^3

    I am trying to do this of one example I have so if you could explain/show workings that would be great.
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  5. #5
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     det \begin{pmatrix} 0-t & 0 & 1 \\ 1 & 0 -t & 0 \\ 0&1&0-t \end{pmatrix}

     det \begin{pmatrix} -t & 0 & 1 \\ 1 &  -t & 0 \\ 0&1&-t \end{pmatrix}

    Sarrus:

    (-t)*(-t)*(-t) + 0*0*0 + 1*1*1 - 1*(-t)*0 - 0*1*(-t) - (-t)*0*1 = -t^3 +1
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