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Math Help - [SOLVED] eigen vectors

  1. #1
    ben35
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    [SOLVED] eigen vectors

    i have found the eigenvalues from

    A= |1 2|
    |5 4|

    as -1 and 6.

    then for the eigenvectors




    then |-5 2| |x1|=0
    |5 -2| |x2|=0

    so x1 = 2/5 x2

    but from here how do i get the eigenvetor of (2/5) ?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ben35 View Post
    i have found the eigenvalues from

    A= |1 2|
    |5 4|

    as -1 and 6.

    then for the eigenvectors




    then |-5 2| |x1|=0
    |5 -2| |x2|=0

    so x1 = 2/5 x2

    but from here how do i get the eigenvetor of (2/5) ?
    You are incorrect about your last step. You sub the eigenvalue into the equation
    \left [ \begin{matrix} 1 & 2 \\ 5 & 4 \end{matrix} \right ] \cdot \left [ \begin{matrix} x_1 \\ x_2 \end{matrix} \right ] = \lambda \left [ \begin{matrix} x_1 \\ x_2 \end{matrix} \right ]

    So for the eigenvalue \lambda = 6 you have:
    \left [ \begin{matrix} 1 & 2 \\ 5 & 4 \end{matrix} \right ] \cdot \left [ \begin{matrix} x_1 \\ x_2 \end{matrix} \right ] = 6 \left [ \begin{matrix} x_1 \\ x_2 \end{matrix} \right ]

    Which says that
    x_1 + 2x_2 = 6x_1
    and
    5x_1 + 4x_2 = 6x_2

    and you can solve this from there.

    -Dan
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