The value of left| begin{array}{ccc} 265 & 24 | vedclass

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(A) Let $\Delta = \left| \begin{array}{ccc} 265 & 240 & 219 \ 240 & 225 & 198 \ 219 & 198 & 181 \end{array} ight|$.Applying $C_1 	o C_1 - C_2$ an

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(A) Let $\Delta = \left| \begin{array}{ccc} 265 & 240 & 219 \ 240 & 225 & 198 \ 219 & 198 & 181 \end{array} ight|$.Applying $C_1 	o C_1 - C_2$ and $C_2 	o C_2 - C_3$:$\Delta = \left| \begin{array}{ccc} 25 & 21 & 219 \ 15 & 27 & 198 \ 21 & 17 & 181 \end{array} ight|$.Applying $C_1 	o C_1 - C_2$:$\Delta = \left| \begin{array}{ccc} 4 & 21 & 219 \ -12 & 27 & 198 \ 4 & 17 & 181 \end{array} ight|$.Applying $R_2 	o R_2 - R_1$ and $R_3 	o R_3 - R_1$:$\Delta = \left| \begin{array}{ccc} 4 & 21 & 219 \ -16 & 6 & -21 \ 0 & -4 & -38 \end{array} ight|$.Alternatively,performing row operations $R_2 	o R_2 - R_1$ and $R_3 	o R_3 - R_2$ on the original matrix:$R_2 	o R_2 - R_1 \implies (240-265, 225-240, 198-219) = (-25, -15, -21)$$R_3 	o R_3 - R_2 \implies (219-240, 198-225, 181-198) = (-21, -27, -17)$Calculating the determinant directly or via reduction yields $\Delta = 0$.

The value of $\left| \begin{array}{ccc} 265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181 \end{array} \right|$ is equal to

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