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Matrix, Find determinant using properties of Det.

  1. Apr 2, 2012 #1
    1. The problem statement, all variables and given/known data
    1 1 1
    a b c = (b-a)(c-a)(c-b)
    a^2 b^2 c^2
    (above is a 3x3 matrix equaling to a equation)
    question:"Show by applying property of the determinant"


    2. Relevant equations
    N/A


    3. The attempt at a solution
    read through the whole chapter of determinants, there were no similar problems. read it the second time focusing on properties, no simimlar properties, Please help.
     
  2. jcsd
  3. Apr 2, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    Start by subtracting the first column from the second and third columns. Then think about an expansion by minors.
     
  4. Apr 2, 2012 #3
    Just solved it. thanks for the reply though.
    1 1 1
    a b c
    a^2 b^2 c^2
    becomes
    1 0 0
    a b-a c-a
    a^2 (b^2-a^2) (c^2-a^2)
    then becomes
    (b-a)(c-a) times
    1 0 0
    a 1 1
    a^2 b-a c-a
    then
    1 0 0
    a 1 0
    a^2 b-a c-b
    det= 1 x 1 x(c-b) ( c-a) (b-a)
     
  5. Apr 2, 2012 #4

    Dick

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    Science Advisor
    Homework Helper

    Yup. That'll do it.
     
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