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Math Help - Eigenvalue/Eigenvector

  1. #1
    Junior Member
    Joined
    Apr 2010
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    Eigenvalue/Eigenvector

    I am loosing my mind. I cannot seem to factor the ^3-4^2-10-12.

    My problem is to verify that e=[1,1,1]^T is an eigenvector of A=(1,2,3), (3,2,1), (2,3,1).

    det(-AI) = (-1)(-2)(-1)+(-2)(-1)(-2)+(-3)(-3)(-3)-(-2)(-2)(-3)-(-1)(-3)(-1)-(-1)(-2)(-3)
    = ^3-4^2-10-12
    = ???
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  2. #2
    MHF Contributor

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    Tejas
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    Re: Eigenvalue/Eigenvector

    since you are given the eigenvector, just calculate:

    \begin{bmatrix}1&2&3\\3&2&1\\2&3&1\end{bmatrix} \begin{bmatrix}1\\1\\1\end{bmatrix} = \begin{bmatrix}6\\6\\6\end{bmatrix}

    this tells you that 6 is an eigenvalue.

    now divide the characteristic polynomial by λ-6.
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