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Math Help - Find Eigenvectors in a 3x3-matrix

  1. #1
    Junior Member
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    Manchester
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    Find Eigenvectors in a 3x3-matrix

    Hi,

    I'm having trouble with finding the eigenvectors of a 3x3 matrix. The matrix M, is defined as the following:
    0 0.3 0.4
    0.6 0 0.6
    0.4 0.7 0





    Having found det(M - I), where I is matrix:
    0 0
    0 0
    0 0





    I have found the following eigenvalues:
    1: 1
    2: -0.6
    3: -0.4

    I am now to find the corresponding eigenvectors, V1, V2, V3, but I can't seem to approach it the right way. I have the following system of equations:

    For 1 = 1:
    0.3y + 0.4z = x
    0.6x + 0.6z = y
    0.4x + 0.7y = z





    And similarly for the remaining eigenvalues.

    How do I go about finding the eigenvectors? ANY help is highly appreciated!
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  2. #2
    Junior Member
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    Between my ears
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    Re: Find Eigenvectors in a 3x3-matrix

    Given the eigenvalues of a matrix, (by definition) to find the corresponding eigenvectors, solve the following system:

    \begin{bmatrix} a11-\lambda & a12& a13 \\  a21& a22-\lambda & a23\\  a31& a32& a33-\lambda  \end{bmatrix}\begin{bmatrix}x1 \\ x2\\ x3\end{bmatrix} = 0

    So, for the first eigenvalue, λ = 1, the system would become as follows:

     \begin{bmatrix} -1& 0.3& 0.4 \\   0.6& -1& 0.6\\  0.4& 0.7& -1 \end{bmatrix}\begin{bmatrix}x1 \\ x2\\ x3\end{bmatrix} = 0

    Solve this equation.

    Then repeat this process for the other two eigenvalues to find the corresponding eigenvectors.
    Last edited by DavidB; September 18th 2013 at 07:25 PM.
    Thanks from topsquark
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