Question

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

• A. 8
• B. – 8
• C. 400
• D. 1

Answer 1

Answer: (B)

– 8

Answer 2

$\left| \begin{matrix} 1^{2} & 2^{2} & 3^{2} \\ 2^{2} & 3^{2} & 4^{2} \\ 3^{2} & 4^{2} & 5^{2} \end{matrix} \right|${Operate

$R_{3} \rightarrow R_{3} - R_{2}$,$R_{2} \rightarrow R_{2} - R_{1}$}

= $\left| \begin{matrix} 1 & 4 & 9 \\ 3 & 5 & 7 \\ 5 & 7 & 9 \end{matrix} \right| = 1(45 - 49) - 4(27 - 35) + 9(21 - 25)$

= $- 4 + 32 - 36 = - 8$.