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Math Help - linear systems - determinant unknowns

  1. #1
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    linear systems - determinant unknowns

    solve the following determinant


    |1 a a^2|
    |1 b b^2|
    |1 c c^2|
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  2. #2
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    Quote Originally Posted by scqlt View Post
    solve the following determinant


    |1 a a^2|
    |1 b b^2|
    |1 c c^2|
    add the opposite of row 1 to row 2 and 3 to get

    \begin{bmatrix}<br />
1 & a & a^2 \\<br />
0 & b-a & b^2-a^2 \\<br />
0 & c-a & c^2 -a^2 \\<br />
\end{bmatrix}

    Now we can expand along the first column to get

    1\cdot ( (b-a)(c^2-a^a)-(c-a)(b^2-a^2)) =

     (b-a)(c-a)(c+a)-(c-a)(b-a)(b+a)=[(b-a)(c-a)][(c+a)-(b+a)]=

    (b-a)(c-a)(c-b)
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