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Help with determinants

  1. Jun 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Express the determinant as a product of four linear factors.

    [itex]
    \left(
    \begin{array}{ccc}
    1 & a & a^3 \\
    1 & b & b^3 \\
    1 & c & c^3
    \end{array}
    \right)
    [/itex]

    I'm sure that the only way to do this without hurting yourself is to operate on the determinant and take factors out. It just doesn't move. I cant see the pattern, I can't see how to get factors out of it. I add rows, columns everything.
     
  2. jcsd
  3. Jun 15, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    Expand along the first row and then just try to factorize it.
     
  4. Jun 15, 2009 #3
    Can't do it. It's hard to show my working on latex buts theres pages of attempts. x^3 I just cant do.
     
  5. Jun 15, 2009 #4

    rock.freak667

    User Avatar
    Homework Helper

    Try row reducing once, with R2-R1 and R3-R1. Then expand along row one.


    then use this identity and see if it helps a3-b3=(a-b)(a2+ab+b2)
     
  6. Jun 15, 2009 #5

    Excellent thanks, thats the identity I needed.
     
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