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Homework Help: How do I get the eigenvectors

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data
    a matrix A:
    [1 3 0
    3 1 0
    0 0 -2]

    Find Q and D where

    QTAQ=D

    3. The attempt at a solution

    I found the eigenvalues of -4,2,2

    When I plug them back in and rref the matrix I only get the trivial solution meaning the matrices are linearly independent. How do I get the eigenvectors if that's the case?
     
  2. jcsd
  3. Dec 9, 2008 #2

    Defennder

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    Homework Helper

    Re: Eigenvectors...

    Check your eigenvalues.
     
  4. Dec 9, 2008 #3
    Re: Eigenvectors...

    [L-1 -3 0
    -3 L-1 0
    0 0 L+2]

    (L+2)((L-1)^2 - 9)
    (L+2)(L^2 -2L +1 -9)
    (L+2)(L^2 -2L -8)
    (L^3 -2L^2 -8L +2L^2 -4L -16)
    L^3 -12L -16
    ...
    meh, got it nevermind. Thanks for the suggestion.
     
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