Question

Find values of x, if
(i)$\begin{vmatrix}2&4\\\2&1\end{vmatrix}$=$\begin{vmatrix}2x&4\\\6&x\end{vmatrix}$

(ii)$\begin{vmatrix}2&3\\\4&5\end{vmatrix}$=$\begin{vmatrix}x&3\\\2x&5\end{vmatrix}$

Answer 1

(i)$\begin{vmatrix}2&4\\\2&1\end{vmatrix}$=$\begin{vmatrix}2x&4\\\6&x\end{vmatrix}$
$\Rightarrow$2x1-5x4=2x x x-6x4
$\Rightarrow$ 2-20=2x2-24
$\Rightarrow$ 2x2=6
$\Rightarrow$ x=±$\sqrt3$

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(ii)$\begin{vmatrix}2&3\\\4&5\end{vmatrix}$=$\begin{vmatrix}x&3\\\2x&5\end{vmatrix}$
$\Rightarrow$ 2x5-3x4=xx5-3x2x
$\Rightarrow$ 10-12=5x-6x
$\Rightarrow$ x=2