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Repeated Eigenvalues

  1. Nov 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve X' = [ [9, 4, 0], [-6, -1, 0], [6, 4, 3]] * X using eigenvalues.


    2. Relevant equations
    (A - λI) * K = 0
    X = eλt


    3. The attempt at a solution
    Set up the characteristic equation to find eigenvalues. I found a root of multiplicity 2 of λ=3 and another distinct root λ=5.

    When setting up equations to solve for the eigenvectors (setting λ= 3) I found:

    6k1 + 4k2 = 0
    -6k1 -4k2 = 0
    6k1 + 4k2 = 0

    So there's only a dependency for k1 and k2. So can't I simply find two linearly independent eigenvectors by substituting different values for k3 such as [2, -3, 1] and [2, -3, 2] and use those as two independent solutions? Or does this mean I still have to walk through the steps of using the Kteλt + Peλt form of the solution to find the second solution for the λ=3 root?
     
  2. jcsd
  3. Nov 24, 2012 #2

    vela

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    Re: Repeated Eigen Values

    Your first method is the right one.
     
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