Question

If $\left|\begin{array}{cc}2x& 5\\ 8& x\end{array}\right|=\left|\begin{array}{cc}6& -2\\ 7& 3\end{array}\right|$, write the value of $x.$

Answer 1

Compute the determinants as shown below:

$\left|\begin{array}{cc}2x& 5\\ 8& x\end{array}\right|=\left|\begin{array}{cc}6& -2\\ 7& 3\end{array}\right|$

$\left(2x\right)\left(x\right)-\left(8\right)\left(5\right)=6\times 3-7\times -2$

${\Rightarrow 2x}^2-40=18+14$

${\Rightarrow 2x}^2-40=32$

${\Rightarrow 2x}^2=72$

${\Rightarrow x}^2=36$

$\Rightarrow x=\pm 6$