The value of left| {begin{array}{ccc} {1^2} & | vedclass

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(B) Let $\Delta = \left| {\begin{array}{ccc} {1^2} & {2^2} & {3^2} \ {2^2} & {3^2} & {4^2} \ {3^2} & {4^2} & {5^2} \end{array}} ight| = \left| {\b

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$-8$

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(B) Let $\Delta = \left| {\begin{array}{ccc} {1^2} & {2^2} & {3^2} \ {2^2} & {3^2} & {4^2} \ {3^2} & {4^2} & {5^2} \end{array}} ight| = \left| {\begin{array}{ccc} 1 & 4 & 9 \ 4 & 9 & 16 \ 9 & 16 & 25 \end{array}} ight|$.Apply row operations: ${R_2} 	o {R_2} - {R_1}$ and ${R_3} 	o {R_3} - {R_2}$.$\Delta = \left| {\begin{array}{ccc} 1 & 4 & 9 \ 4-1 & 9-4 & 16-9 \ 9-4 & 16-9 & 25-16 \end{array}} ight| = \left| {\begin{array}{ccc} 1 & 4 & 9 \ 3 & 5 & 7 \ 5 & 7 & 9 \end{array}} ight|$.Expanding along the first row:$\Delta = 1(5 	imes 9 - 7 	imes 7) - 4(3 	imes 9 - 7 	imes 5) + 9(3 	imes 7 - 5 	imes 5)$$\Delta = 1(45 - 49) - 4(27 - 35) + 9(21 - 25)$$\Delta = 1(-4) - 4(-8) + 9(-4)$$\Delta = -4 + 32 - 36 = -8$.

The value of $\left| {\begin{array}{ccc} {1^2} & {2^2} & {3^2} \\ {2^2} & {3^2} & {4^2} \\ {3^2} & {4^2} & {5^2} \end{array}} \right|$ is

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