Question

If $A=\left[\begin{array}{cc}\log x& -1\\ -\log x& 2\end{array}\right]$ and if $\text{det}\left(A\right)=2$ , then the value of $x$ is equal to :

• A. $2$
• B. $e^2$
• C. $-2$
• D. $e$
• E. $\log 2$

Answer 1

The correct option is B $e^2$

Given, $A=\left[\begin{array}{cc}\log x& -1\\ -\log x& 2\end{array}\right]$
Therefore, $|A|=\left|\begin{array}{cc}\log x& -1\\ -\log x& 2\end{array}\right|$
$\Rightarrow 2=2\log x-\log x$
$\Rightarrow 2=\log x$
$\therefore x=e^2$