1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    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

    User Avatar
    Science Advisor
    Homework Helper

    Yup. That'll do it.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook