Question

If $A = \begin{bmatrix}log\,x&-1\\ -log\,x&2\end{bmatrix}$ and if $det (A) = 2$, then the value of $x$ is equal to

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

Answer 1

Answer: (B)

Given, $A=\begin{bmatrix}\log x & -1 \\ -\log x & 2\end{bmatrix}$
$\therefore |A|=\begin{bmatrix}\log x & -1 \\ -\log x & 2\end{bmatrix}$
$=2 \log x-\log x=\log x$
But it is given, $\operatorname{det}(A)=|A|=2$
$\therefore 2=\log x \Rightarrow x=e^{2}$