A) 8
B) \[-8\]
C) 400
D) 1
E) 0
Correct Answer: B
Solution :
\[\left| \begin{matrix} {{1}^{2}} & {{2}^{2}} & {{3}^{2}} \\ {{2}^{2}} & {{3}^{2}} & {{4}^{2}} \\ {{3}^{2}} & {{4}^{2}} & {{5}^{2}} \\ \end{matrix} \right|\] \[=\left| \begin{matrix} 1 & 4 & 9 \\ 4 & 9 & 16 \\ 9 & 16 & 25 \\ \end{matrix} \right|=\left| \begin{matrix} 1 & 3 & 5 \\ 4 & 5 & 7 \\ 9 & 7 & 9 \\ \end{matrix} \right|\] \[{{C}_{2}}\to {{C}_{2}}-{{C}_{1}}and\,{{C}_{3}}\to {{C}_{3}}-{{C}_{2}}\] \[=\left| \begin{matrix} 1 & 3 & 2 \\ 4 & 5 & 2 \\ 9 & 7 & 2 \\ \end{matrix} \right|\] \[{{C}_{3}}\to {{C}_{3}}-{{C}_{2}}\] \[=\left| \begin{matrix} 1 & 3 & 2 \\ 3 & 2 & 0 \\ 5 & 2 & 0 \\ \end{matrix} \right|\] \[\begin{align} & {{R}_{2}}\to {{R}_{2}}-{{R}_{1}} \\ & {{R}_{3}}\to {{R}_{3}}-{{R}_{2}} \\ \end{align}\] \[=2\left| \begin{matrix} 3 & 2 \\ 5 & 2 \\ \end{matrix} \right|=2(6-10)=-8\]
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