Question

Find the values of x, if

$\left|\begin{array}{cc}x+1& x-1\\ x-3& x+2\end{array}\right|=\left|\begin{array}{cc}4& -1\\ 1& 3\end{array}\right|$

Answer 1

$\left|\begin{array}{cc}x+1& x-1\\ x-3& x+2\end{array}\right|=\left|\begin{array}{cc}4& -1\\ 1& 3\end{array}\right|$

Expanding det on both sides.

$\Rightarrow (x+1)(x+2)-(x-1)(x-3)=12+1$

$\Rightarrow x^2+3x+2-x^2+4x-3=13$

$\Rightarrow 7x=14$

$\therefore x=2$