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Math Help - Find the value of determinant

  1. #1
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    Find the value of determinant

    If x,y,z are all different and given that \Rightarrow  \begin{vmatrix}    x  & x^2 & 1+x^3  \\    y & y^2 & 1+y^3 \\   z & z^2 & 1+z^3   \end{vmatrix}  =0   Determine the value of (1+xyz).........
    Last edited by Shivanand; December 17th 2008 at 01:07 AM.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi,

    Hint : recall (or show that) \begin{vmatrix} 1 & x & x^2\\ 1 & y & y^2 \\ 1 & z & z^2\end{vmatrix}=(z-y)(z-x)(y-x).
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  3. #3
    Moo
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    Hello,
    Quote Originally Posted by Shivanand View Post
    If x,y,z are all different and given that \Rightarrow  \begin{vmatrix}    x  & x^2 & 1+x^3  \\    y & y^2 & 1+y^3 \\   z & z^2 & 1+z^3   \end{vmatrix}  =0   Determine the value of (1+xyz).........
    Can you figure out that the determinant is (x-y)(y-z)(z-x)(1+xyz) ?
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