Question:
If $\left|\begin{array}{ll}x+1 & x-1 \\ x-3 & x+2\end{array}\right|=\left|\begin{array}{cc}4 & -1 \\ 1 & 3\end{array}\right|$, then write the value of $x$.
Solution:
$\left|\begin{array}{cc}x+1 & x-1 \\ x-3 & x+2\end{array}\right|=\left|\begin{array}{cc}4 & -1 \\ 1 & 3\end{array}\right|$
$\Rightarrow(x+1)(x+2)-(x-1)(x-3)=12+1$
$\Rightarrow x^{2}+3 x+2-x^{2}+4 x-3=13$
$\Rightarrow 7 x-1=13$
$\Rightarrow 7 x=14$
$\Rightarrow x=2$
Hence, the value of $x$ is 2 .
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