Question:
Find the value of $x$ from the following: $\left|\begin{array}{cc}x & 4 \\ 2 & 2 x\end{array}\right|=0$
Solution:
$\left|\begin{array}{cc}x & 4 \\ 2 & 2 x\end{array}\right|=0$
$\Rightarrow 2 x^{2}-8=0$
$\Rightarrow 2 x^{2}=8$
$\Rightarrow x^{2}=\frac{8}{2}=4$
$\Rightarrow x=\sqrt{4}=\pm 2$