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Determinant question

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Hi,
    i'm trying to solve this problem:

    http://img4.imageshack.us/img4/3876/53065718.jpg [Broken].[/URL]


    3. The attempt at a solution

    I have shown it for n=2 and n=3 then I was going to use induction to prove it for all n, but I can't seem to find a way to do it. Please help!

    Thanks.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 26, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    If you expand the determinant along the last column, then you will get terms of the form
    [tex]a_i^n \begin{vmatrix}
    1 & a_2 & a_2^2 & \cdots & a_2^{n-1} \\
    1 & a_3 & a_3^2 & \cdots & a_3^{n-1} \\
    \vdots & \cdots & \cdots & \cdots & \cdots \\
    1 & a_{n} & a_n^2 & \cdots & a_n^{n-1} \\
    \end{vmatrix}[/tex]
     
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