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Determinant Properties

  1. Aug 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Show without evaluating the determinant the equality.



    2. Relevant equations


    [itex]

    \left(
    \begin{array}{ccc}
    1 & a & bc \\
    1 & b & ac \\
    1 & c & ab
    \end{array}
    \right)

    [/itex]

    =

    [itex]

    \left(
    \begin{array}{ccc}
    1 & a & a^2 \\
    1 & b & b^2 \\
    1 & c & c^2
    \end{array}
    \right)

    [/itex]

    3. The attempt at a solution

    I tried the facts of determinants - I did column 3 plus column 2. I can't see it. This is actually a Question on Boas 3rd Ed. Chapter 3 Section 3 No. 7.
     
    Last edited: Aug 9, 2009
  2. jcsd
  3. Aug 10, 2009 #2

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    (The brackets that you are using is generally used for matrices; for a determinant, vertical lines are used to enclose it.)

    Multiply the first row by 'a' and get 1/a outside. The 1st row becomes |a a^2 abc|. Now think what you can multiply the 2nd and 3rd rows with.

    After that, take out something common from a column.

    Then interchange columns or do a cyclic permutation on the columns, keeping track of the sign of the determinant. You will get the answer.

    For any help, don't hesitate to ask.
     
  4. Aug 10, 2009 #3
    Yeah, I actually just copied and pasted that from somewhere here that I searched for, sorry, I don't know LATEX. Thanks, I will try your suggestion.
     
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