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Math Help - Eigenvalues/Eigenvectors

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    Eigenvalues/Eigenvectors

    How do you find the characteristic polynomial, eigenvalues, and eigenvectors of the following matrix?

    \begin{pmatrix}2&-2&3\\0&3&-2\\0&-1&2\end{pmatrix}
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  2. #2
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    Quote Originally Posted by logitech View Post
    How do you find the characteristic polynomial, eigenvalues, and eigenvectors of the following matrix?

    \begin{pmatrix}2&-2&3\\0&3&-2\\0&-1&2\end{pmatrix}
    In the usual way (you will find many solved problems like this one by searching the MHF forums or doing a Google search).

    Start by calculating \det \begin{pmatrix}2 - \lambda & -2 & 3 \\ 0 & 3 - \lambda &-2\\0 & -1 & 2 - \lambda\end{pmatrix} (I suggest expanding down the first column).

    Then solve \det \begin{pmatrix}2 - \lambda & -2 & 3 \\ 0 & 3 - \lambda &-2\\0 & -1 & 2 - \lambda\end{pmatrix} = 0 etc.

    Please post what you've done and exactly where you get stuck.
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