Question

If $\left|\begin{array}{cc}x+1& x-1\\ x-3& x+2\end{array}\right|=\left|\begin{array}{cc}4& -1\\ 1& 3\end{array}\right|$, then write the value of $x$.

Answer 1

Compute the determinants as shown below:

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

$(x+1)(x+2)-(x-3)(x-1)=4\times 3-1\times -1$

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

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

$\Rightarrow 7x-1=13$

$\Rightarrow 7x=14$

$\Rightarrow x=2$