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Homework Help: Finding eigenvectors?

  1. Mar 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Given the characteristic polynomial -2+x-2x^2-x^3, find the eigenvalues and eigenvectors of the matrix [-1, -1, 0] [1, 1, 1] [3, 1, -2]

    2. Relevant equations

    3. The attempt at a solution

    The eigenvalues are -2.659, 0.329-.802i, and 0.329+.802i. Next you plug each eigenvalue into the matrix A-xI to solve the system (A-xI)v=0 and find the eigenvectors. Then you solve the system by reducing the matrix to row echelon form. However, when I do that I get the identity matrix. So then what are the eigenvectors?
  2. jcsd
  3. Mar 9, 2009 #2


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    Homework Helper

    That occurs often when the eigenvalues are not close enough. You either need to switch to a less sensitive method, or find closer approximations to the eigenvalues.
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