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Math Help - eigenvectors

  1. #1
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    eigenvectors

    Hi,
    I have a probelm in finding eigenvectors. For example, we have a matrix:
    1 2
    3 2

    The eignevalues for this are x = -1 and x = 4. I understand how to find the eigenvector when x = -1. But when x = 4, we get:
    Code:
    -3 2 y 0 * = 3 -2 z 0
    which, when multiplied by means that 3y - 2z = 0 (using (A-xI)v=0). Now the final answer is:
    Code:
    2y v = 3y
    How??
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by alireza1989 View Post
    Hi,
    I have a probelm in finding eigenvectors. For example, we have a matrix:
    1 2
    3 2

    The eignevalues for this are x = -1 and x = 4. I understand how to find the eigenvector when x = -1. But when x = 4, we get:
    Code:
    -3 2 y 0 * = 3 -2 z 0
    which, when multiplied by means that 3y - 2z = 0 (using (A-xI)v=0). Now the final answer is:
    Code:
    2y v = 3y
    How??
    What are you doing with that last matrix?

    \left ( \begin{matrix} 1 & 2 \\ 3 & 2 \end{matrix} \right ) \cdot \left ( \begin{matrix} y \\ z \end{matrix} \right ) = \lambda \left ( \begin{matrix} y \\ z \end{matrix} \right )
    for both of your eigenvalues.

    You do not use the matrix
    \left ( \begin{matrix} 1 - \lambda & 2 \\ 3 & 2 - \lambda \end{matrix} \right )
    to find your eigenvectors.

    -Dan
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  3. #3
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    Joined
    May 2008
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    I found out how to do it.
    Thanx
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