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Eigenvalues of a 3x3 Matrix

  1. Nov 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Given the matrix A=

    1 -1 -1
    -1 1 -1
    -1 -1 1

    Find the eigenvalues.


    2. Relevant equations

    I = identity matrix

    3. The attempt at a solution

    det(A-xI) = (1-x)3 - 2 - 3*(1-x) = 0 ⇔
    ⇔(1-x)3 - 3*(1-x) - 2 = 0

    I can't find a way to solve this equation...
    Any help would be appreciated!4

    Daniel
     
    Last edited by a moderator: Nov 8, 2012
  2. jcsd
  3. Nov 8, 2012 #2

    Mentallic

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    Homework Helper

    If you let y=1-x, then the cubic [itex]y^3-3y-2[/itex] has a zero at y=2.
     
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