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Eigenvalues? DO I have the right idea with this problem?

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm supposed to find all the eigenvalues for this 2x2 matrix:

    0 2
    3 0

    2. Relevant equations



    3. The attempt at a solution

    When I tried to do it with no row interchanges, I got the characteristic characteristic equation:
    λ2-6=0

    So, instead of solving this, I interchanged the rows of my matrix to get:

    3 0
    0 2
    And then my determinant would be negative right? I got λ=2,3...I was wondering if I did this right?

    Any help is appreciated, thanks.
     
  2. jcsd
  3. Dec 11, 2011 #2

    Mark44

    Staff: Mentor

    Which means that the eigenvalues are ±√6.
    The latter part is wrong.

    The determinant you are investigating is
    [tex]\begin{vmatrix}-\lambda & 2 \\ 3 & -\lambda \end{vmatrix}[/tex]

    not
    [tex]\begin{vmatrix}0 & 2 \\ 3 & 0 \end{vmatrix}[/tex]
     
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