left| {begin{array}{ccc} 1/a & a^2 & bc 1/b | vedclass

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(D) To evaluate the determinant $\Delta = \left| {\begin{array}{ccc} 1/a & a^2 & bc \ 1/b & b^2 & ca \ 1/c & c^2 & ab \end{array}} ight|$,we multi

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$0$

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(D) To evaluate the determinant $\Delta = \left| {\begin{array}{ccc} 1/a & a^2 & bc \ 1/b & b^2 & ca \ 1/c & c^2 & ab \end{array}} ight|$,we multiply and divide by $abc$:$\Delta = \frac{1}{abc} \left| {\begin{array}{ccc} 1 & a^3 & abc \ 1 & b^3 & abc \ 1 & c^3 & abc \end{array}} ight|$Now,take $abc$ common from the third column:$\Delta = \frac{abc}{abc} \left| {\begin{array}{ccc} 1 & a^3 & 1 \ 1 & b^3 & 1 \ 1 & c^3 & 1 \end{array}} ight|$Since the first column and the third column are identical,the value of the determinant is $0$.

$\left| {\begin{array}{ccc} 1/a & a^2 & bc \\ 1/b & b^2 & ca \\ 1/c & c^2 & ab \end{array}} \right| = $

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