Question

Let $S =\{\sqrt{ n }: 1 \leq n \leq 50$ and $n$ is odd $\}$ Let $a \in S$ and $A =\begin{bmatrix}1 & 0 & a \\ -1 & 1 & 0 \\ - a & 0 & 1\end{bmatrix}$ If $\displaystyle\sum_{ a \in S } \text{det}(\text{adj} A )=100 \lambda$, then $\lambda$ is equal to

• A. 218
• B. 221
• C. 663
• D. 1717

Answer 1

Answer: (B)

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