Question

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

• A. 2
• B. $e^2$
• C. -2
• D. $e$
• E. $log2$

Answer 1

Answer: (B)

Given, $A=\left[\begin{array}{cc}\log x& -1\\ -\log x& 2\end{array}\right]$
$\therefore |A|=\left[\begin{array}{cc}\log x& -1\\ -\log x& 2\end{array}\right]$
$=2\log x-\log x=\log x$
But it is given, $\det (A)=|A|=2$
$\therefore 2=\log x\Rightarrow x=e^2$