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Find the value of x from the following : $\begin {vmatrix} x & 4 \\ 2 & 2x \end {vmatrix} = 0$

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Toolbox:
• A determinant of order $2\times 2$ can be evaluated as $\begin{vmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{vmatrix}$
• $\mid A\mid=a_{11}a_{22}-a_{21}a_{12}$
$\begin {vmatrix} x & 4 \\ 2 & 2x \end {vmatrix} = 0$
On expanding we get,
$2x^2-8=0$
$\Rightarrow 2x^2=8$
$x^2=\large\frac{8}{2}$
$x^2=4$
$x=\pm 2$
answered Sep 20, 2013