Question

Matrix $A_{r}=\begin{bmatrix}r & r & -1 \\ r & -1 & r\end{bmatrix} ; r=1,2,3, \ldots .$ If $\displaystyle\sum_{r=1}^{100}\left|A_{r}\right|$, then $K =\ldots \ldots \ldots \ldots\left(\left|A_{r}\right|=det\left(A_{r}\right)\right)$

• A. 2
• B. 6
• C. 4
• D. 8

Answer 1

Answer: (D)

$\left|A_{r}\right|=2 r -1$
$\displaystyle\sum_{r=1}^{100}(2 r -1)=1+3+\ldots+199=10000=10^{k / 2}$
$\Rightarrow \frac{k}{2}=4$
$\Rightarrow k =8$