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Eigenvector problem

  1. Oct 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the eigenvalues and eigenvectors of [tex] \left( \begin{array}{ccc} 2 & 0 & 0 \\ 0 & 3 & 4 \\ 1 & 1 & 0 \end{array} \right)[/tex]

    2. Relevant equations

    [tex]p(\lambda) = det(A - \lambda I) = 0 [/tex]

    3. The attempt at a solution

    [tex]A - \lambda I = \left( \begin{array}{ccc} 2-\lambda & 0 & 0 \\ 0 & 3-\lambda & 4 \\ 1 & 1 & 0 \end{array} \right)[/tex]

    [tex]det(A - \lambda I) = (2 - \lambda)(-4) + 1 = 0[/tex]

    [tex]-8 + 4 \lambda + 1 = 0[/tex]

    [tex]4\lambda = 7[/tex]

    [tex]\lambda = \frac{4}{7}[/tex]

    [tex]A - \lambda I = \left( \begin{array}{ccc} \frac{1}{4} & 0 & 0 \\ 0 & \frac{5}{7} & 4 \\ 1 & 1 & 0 \end{array} \right)[/tex]

    [tex]\frac{1}{4}x_1 = 0[/tex]

    [tex]\frac{5}{4}x_2 + 4x_3 = 0[/tex]

    Eigenvector = [tex]\left( \begin{array}{ccc} 0 \\ 0 \\ 0 \end{array} \right)[/tex]
     
    Last edited: Oct 26, 2009
  2. jcsd
  3. Oct 26, 2009 #2

    Mark44

    Staff: Mentor

    This should be in the Calculus and Beyond section.

    For your formatting problems, use [ tex ] and [ /tex ] tags (without the extra spaces I put in, instead of the inline LaTeX tags, [ itex ], you used.
     
  4. Oct 26, 2009 #3
    Thanks. Should I repost this in the other section?
     
  5. Oct 26, 2009 #4

    Pengwuino

    User Avatar
    Gold Member

    As for the problem, in your [tex]A-\lambda I[/tex] matrix, you still have a [tex]-\lambda[/tex] in the 3rd row, 3rd column entry. It isn't simply 0.
     
  6. Oct 26, 2009 #5
    Oh, you're right. Thanks!
     
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