left| {begin{array}{ccc} 19 & 17 & 15 9 & 8 | vedclass

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(A) To evaluate the determinant $\Delta = \left| {\begin{array}{ccc} 19 & 17 & 15 \ 9 & 8 & 7 \ 1 & 1 & 1 \end{array}} ight|$,we can use row opera

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$0$

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(A) To evaluate the determinant $\Delta = \left| {\begin{array}{ccc} 19 & 17 & 15 \ 9 & 8 & 7 \ 1 & 1 & 1 \end{array}} ight|$,we can use row operations to simplify it.Apply the operation $C_1 	o C_1 - C_2$ and $C_2 	o C_2 - C_3$:$\Delta = \left| {\begin{array}{ccc} 19-17 & 17-15 & 15 \ 9-8 & 8-7 & 7 \ 1-1 & 1-1 & 1 \end{array}} ight| = \left| {\begin{array}{ccc} 2 & 2 & 15 \ 1 & 1 & 7 \ 0 & 0 & 1 \end{array}} ight|$.Now,expand along the third row $(R_3)$:$\Delta = 0 - 0 + 1 	imes \left| {\begin{array}{cc} 2 & 2 \ 1 & 1 \end{array}} ight| = 1 	imes (2 	imes 1 - 2 	imes 1) = 1 	imes (2 - 2) = 0$.Thus,the value of the determinant is $0$.

$\left| {\begin{array}{ccc} 19 & 17 & 15 \\ 9 & 8 & 7 \\ 1 & 1 & 1 \end{array}} \right| = $

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