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    I am lost and need guidance :/
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    (Original post by Chinese Noodles)
    I am lost and need guidance :/
    To find an eigenvector corresponding to an eigenvalue  \lambda you need to find a vector  (x, y, z)^T satisfying:

     \begin{pmatrix} {0-\lambda} & {-1} & {1} \\5 & {-2-\lambda} & {-1} \\{-8} & 0 & {5 - \lambda} \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end {pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}

    If you don't know how to do this, multiply out the LHS to get three simultaneous equations and solve them in terms of a parameter.

    EDIT: Corrected my matrix.
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    this should help:

    https://www.scss.tcd.ie/Rozenn.Dahyo...utionEigen.pdf
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    (Original post by 16Characters....)
    To find an eigenvector corresponding to an eigenvalue  \lambda you need to find a vector  (x, y, z)^T satisfying:

     \begin{pmatrix} {0-\lambda} & {-1} & {1} \\5 & {-2-\lambda} & {-1} \\{-8} & 0 & {5 - \lambda} \end{pmatrix} \begin{pmatrix} x \\ y \\ z \end {pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}

    If you don't know how to do this, multiply out the LHS to get three simultaneous equations and solve them in terms of a parameter.

    EDIT: Corrected my matrix.
    i got the cubic equation where x = lamnda


    x^3 + 2x^2 -18x -1 = 0



    doesnt give integers :/ one of the soloution is 1
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    (Original post by Chinese Noodles)
    i got the cubic equation where x = lamnda


    x^3 + 2x^2 -18x -1 = 0



    doesnt give integers :/ one of the soloution is 1
    How did you get that equation?
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    (Original post by 16Characters....)
    How did you get that equation?
    ok i got x^3 + 3x^2 + 3x -1 = 0 now




    still no luck



    i just used the determinant method
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    (Original post by Chinese Noodles)
    ok i got x^3 + 3x^2 + 3x -1 = 0 now




    still no luck



    i just used the determinant method
    So you are trying to find the eigenvalues? OK I thought you were looking for the eigenvector.

    If so you are one sign wrong, the characteristic equation should be  \lambda^3 - 3\lambda^2 + 3 \lambda - 1 = 0 .
 
 
 
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