Results 1 to 2 of 2

Math Help - Eigenvalues for 3x3 Matrix

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    156

    Eigenvalues for 3x3 Matrix

    Trying to find eigenvalues for this matrix A - \lambda I

    \left(\begin{array}{ccc}{1 - \lambda} & 2 & {-2} \\ 2 & {1 - \lambda} & 0 \\ {-2} & 0 & {1 - \lambda} \end {array} \right)

    If my math is correct, the determinant of this is {(1-\lambda)}^3 - 8\lambda - 12, but this doesn't factor, so I don't know how to find the roots.

    Can somebody help? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,401
    Thanks
    762

    Re: Eigenvalues for 3x3 Matrix

    your math is incorrect.

    the determinant is:

    (1 - λ)3 - (-2)(-2)(1 - λ) - (2)(2)(1 - λ) = 1 - 3λ + 3λ2 - λ3 - 8(1 - λ) = -7 +5λ + 3λ2 - λ3

    this has one rational root, and two irrational roots which are "conjugate" (in the sense of square roots).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 27th 2010, 03:07 PM
  2. Eigenvalues of a 3x3 matrix
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 4th 2009, 09:44 PM
  3. Matrix eigenvalues
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 29th 2009, 07:27 AM
  4. Eigenvalues of a 3*3 Matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 7th 2008, 02:10 AM
  5. 3x3 Matrix - Eigenvalues
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: October 2nd 2008, 10:06 AM

Search Tags


/mathhelpforum @mathhelpforum