Question

Let $S=\{\sqrt{n}:1\le n\le 50$ and $n$ is odd $\}$ Let $a\in S$ and $A=\left[\begin{array}{ccc}1& 0& a\\ -1& 1& 0\\ -a& 0& 1\end{array}\right]$ If $\sum _{a\in S}\text{det}(\text{adj}A)=100\lambda$, then $\lambda$ is equal to

• A. 218
• B. 221
• C. 663
• D. 1717

Answer 1

Answer: (B)

$S=\{\sqrt{n}:1\le n\le 50$ and $n$ is odd $\}$
$=\{\sqrt{1},\sqrt{3},\sqrt{5}\dots \dots \dots \sqrt{49}\},25$ terms
$|A|=1+a^2$
$\sum _{a\subseteq }\text{det}(\text{adj}A)=\sum _{a\in S}|A{|}^2=\sum {\left(1+a^2\right)}^2$
$=22100=100\lambda$
$\lambda =221$