Question

Find the values of $x$, if
(i)$\left|\begin{array}{cc}2& 4\\ 5& 1\end{array}\right|=\left|\begin{array}{cc}2x& 4\\ 6& x\end{array}\right|$ (ii)$\left|\begin{array}{cc}2& 3\\ 4& 5\end{array}\right|=\left|\begin{array}{cc}x& 3\\ 2x& 5\end{array}\right|$

Answer 1

(i)$\left|\begin{array}{cc}2& 4\\ 5& 1\end{array}\right|=\left|\begin{array}{cc}2x& 4\\ 6& x\end{array}\right|$

$\Rightarrow 2-20=2x^2-24$

$\Rightarrow 2x^2=6$

$\Rightarrow x^2=3$

$\Rightarrow x=\pm \sqrt{3}$

(ii)$\left|\begin{array}{cc}2& 3\\ 4& 5\end{array}\right|=\left|\begin{array}{cc}x& 3\\ 2x& 5\end{array}\right|$

$\Rightarrow 10-12=5x-6x$

$\Rightarrow -2=-x$

$\Rightarrow x=2$