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Eigenvector Woes

  1. Oct 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the eigenvectors of: ##
    \newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr}

    5 & 0 & \sqrt{3} \\

    0 & 3 & 0 \\

    \sqrt{3} & 0 & 3

    \end{array}\right)

    ##
    2. Relevant equations

    ##(\mathbf{A}-\lambda\mathbf{I})\cdot\mathbf{x}=0##

    3. The attempt at a solution

    I get the correct eigenvectors for ##\lambda=2,6##, but I don't understand why the eigenvector is ##\hat{j}## when ##\lambda=3##.

    When ##\lambda=3##, the matrix becomes ##
    \newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrr}

    2 & 0 & \sqrt{3} \\

    0 & 0 & 0 \\

    \sqrt{3} & 0 & 0

    \end{array}\right)

    ##. The first row yields a function ##2x-\sqrt{3}z=0##. The points that satisfy this equation do not lay along ##\hat{j}##. What am I missing?

    Thanks,
    Chris
     
  2. jcsd
  3. Oct 25, 2014 #2

    vela

    User Avatar
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    The third row implies ##x=0##. Do you see that?
     
  4. Oct 25, 2014 #3

    Mark44

    Staff: Mentor

    The first row yields the equation 2x + 3 √ z=0.

    As vela notes, the third row implies that x = 0. Neither equation involves y, so there are no constraints on y.
     
  5. Oct 25, 2014 #4
    Ah, that makes sense.

    Thanks,
    Chris
     
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