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Help with eigenvalues from matrix

  1. Jul 1, 2011 #1
    1. The problem statement, all variables and given/known data
    find the eignevalues (a part of a larger problem) for

    A= | -4 1 1 |
    | 1 5 -1 |
    | 0 1 -3 |


    2. Relevant equations



    3. The attempt at a solution

    = | -4-x 1 1 |
    | 1 5-x -1 |
    | 0 1 -3-x |

    (-4-x)[ (5-x)(-3-x) + 1 ] - (1)[ (1)(-3-x) - 0] + (1)[1-0]

    (-4-x)[ x^2 -2x -14] + x + 4

    (-4)[-x^3 + 2x^2 + 14x] + x + 4

    4x^3 - 8x^2 - 56x + x + 4

    4x^3 - 8x^2 - 55x + 4

    I do not see the roots for the above being -3, -4, and 5.


    The book has x1 = -3, x2 = -4, and x3 = 5.

    When I run the eigenvalue routine in the software package Maxima, I believe I am getting (-3 -4,5) - output is a little confusing. - anyway I am seeing the same numbers

    When I expand (x+3)(x+4)(x-5)

    I get 3x^3 - 3x^2 - 60x.

    Help?

    Thanks
    Sparky_
     
  2. jcsd
  3. Jul 1, 2011 #2

    gb7nash

    User Avatar
    Homework Helper

    Found it. You're not properly multiplying (-4-x) by [ x^2 -2x -14]. Unfortunately, you can't just multiply by the -x and then by -4 (I wish you could). Instead:

    (-4-x)[ x^2 -2x -14] = (-4)[ x^2 -2x -14] - x[ x^2 -2x -14] = ...
     
  4. Jul 1, 2011 #3
    Crap - (embarrassed)

    it's been too long since I've done this - out of practice

    Thanks for the help!
     
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