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Computing eigenvalues and eigenvectors

  1. Jul 27, 2010 #1
    Find the characteristic polynomial, eigenvectors, and eigenvalues of the matrix.

    Code (Text):

    [
    2 -2 3
    0 3 -2
    0 -1 2
    ]
    My characteristic poly is x^3 - 7x^2 + 14x - 8

    The roots are 1, 2, and 4.

    When solving the system, (2I - A)x = 0 I get:
    Code (Text):

    [
    0 1 0 0
    0 0 1 0
    0 0 0 0
    ]
     
    Can someone tell me how this relates to a solution?

    It looks like x2 and x3 would be zero, but what about x1?
     
  2. jcsd
  3. Jul 27, 2010 #2
    This means that (t 0 0) is an eigenvector for any t. Since constant multiples of eigenvectors are also eigenvectors, typically we would say that (1 0 0) is the eigenvector (associated with the eigenvalue 2).
     
  4. Jul 27, 2010 #3
    Thanks, that makes sense.
     
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