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Determinant of 3x3 Matrix without direct evaluation

  1. Feb 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that:

    (x^2) (2x) (-2)
    (2x) (2-x^2) (2x)
    (2) (-2x) (-x^2)

    = (x^2 + 2)^3

    Do not use direct evaluation.


    2. Relevant equations



    3. The attempt at a solution

    As direct evaluation is not permitted, I'm wondering which method should I use? Thank you
     
  2. jcsd
  3. Feb 2, 2012 #2
    what possible methods do you have in mind?
     
  4. Feb 2, 2012 #3
    Is it a method using cofactors?
     
  5. Feb 2, 2012 #4
    okay, now what does the method of cofactors do?
     
  6. Feb 2, 2012 #5
    I'm going to have to look into that.

    I have a sheet which I just got today from lecture and it states;

    Cofactor is the minor multiplied by the sign of the element
    Cij = (-1)^(i+j) Mij
     
  7. Feb 3, 2012 #6
    Is this cofactor method different from making an upper triangular matrix from it?
     
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