Question

If $\left|\begin{array}{cc}3x& 7\\ -2& 4\end{array}\right|=\left|\begin{array}{cc}8& 7\\ 6& 4\end{array}\right|$, find the value of $x.$

Answer 1

Compute the determinants as shown below:

$\left|\begin{array}{cc}3x& 7\\ -2& 4\end{array}\right|=\left|\begin{array}{cc}8& 7\\ 6& 4\end{array}\right|$

$\left(3x\right)\left(4\right)-(-2)\left(7\right)=8\times 4-6\times 7$

$\Rightarrow 12x+14=32-42$

$\Rightarrow 12x=-10-14$

$\Rightarrow 12x=-24$

$\Rightarrow x=-2$