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Math Help - How to find the eigenvalues of a 3x3 matrix

  1. #1
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    Mar 2009
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    How to find the eigenvalues of a 3x3 matrix

    [1 1 1]
    [1 1 1]
    [1 1 1]

    1) why can't i just do guassian elimination to make it
    [1 1 1]
    [0 0 0]
    [0 0 0] then the eigenvalues would be 1, 0

    2) if i just do it straight i get
    [1-λ 1 1]
    [1 1-λ 1]
    [1 1 1-λ] and then i get

    (1-λ)( (1-λ)(1-λ) - 1 ) - (1)( (1)(1-λ)-1 ) + (1)(1-(1-λ))

    and it simplifies to -2 + λ + 3λ^2 - λ^3

    how do i get the eigenvalues from here?

    thanks
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  2. #2
    Senior Member
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    Paris
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    Quote Originally Posted by cnix View Post
    then the eigenvalues would be 1, 0
    Due to the paricular form of the matrix, one can see that

    \begin{pmatrix}1&1&1\\1&1&1\\1&1&1\\\end{pmatrix}\  begin{pmatrix}1\\1\\1\\\end{pmatrix}=3\begin{pmatr  ix}1\\1\\1\\\end{pmatrix}

    and it simplifies to -2 + λ + 3λ^2 - λ^3
    That's wrong. The roots of the polynomial you will find are the eigenvalues.
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