Evaluate the determinant: left| begin{array}{ | vedclass

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(A) Let $\Delta = \left| \begin{array}{ccc} 1/a & 1 & bc \ 1/b & 1 & ca \ 1/c & 1 & ab \end{array} ight|$.Multiply $R_1$ by $a$,$R_2$ by $b$,and $

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Let $\Delta = \left| \begin{array}{ccc} 1/a & 1 & bc \ 1/b & 1 & ca \ 1/c & 1 & ab \end{array} ight|$.Multiply $R_1$ by $a$,$R_2$ by $b$,and $R_3$ by $c$,and divide the determinant by $abc$:$\Delta = \frac{1}{abc} \left| \begin{array}{ccc} 1 & a & abc \ 1 & b & abc \ 1 & c & abc \end{array} ight|$.Take $abc$ common from the third column:$\Delta = \frac{abc}{abc} \left| \begin{array}{ccc} 1 & a & 1 \ 1 & b & 1 \ 1 & c & 1 \end{array} ight|$.Since the first and third columns are identical,the value of the determinant is $0$.

Evaluate the determinant: $\left| \begin{array}{ccc} 1/a & 1 & bc \\ 1/b & 1 & ca \\ 1/c & 1 & ab \end{array} \right|$

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