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Finding values that make a determinate = 0

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Given the matrix A = {a, 3, 8}{a, -3, 4}{7, -4, a} find all values of a that make det(A) = 0.

    (each {} is a row in the matrix, 3x3)

    3. The attempt at a solution

    I've expanded it out using the Cofactor theorem, ie. a11c11 + a21c21 + a31c31, and I come out with a polynomial, -2(3a^2+8a-126) which I equate to 0. Solving for the quadratic gives ugly roots which I can't see being correct.

    Thanks for any help
     
  2. jcsd
  3. Oct 16, 2009 #2

    whs

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    Doing a very quick calculation, are you sure your '-126' shouldn't be '126'? (When you factor out the -2, shouldn't you have a positive 126 left?)
     
  4. Oct 16, 2009 #3

    nicksauce

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    Well according to maple your determinant is correct. You should really trust the math instead of your intuition about what you can see being correct.
     
  5. Oct 16, 2009 #4
    Huh, it was correct :P I just figured the answer would be integers. Thanks for the help :)
     
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