Let \(a, b, c, d \in \mathbf{R}\) be such that \(a d-b c \neq 0\) and \(e\) be a positive number other than 1 . If \(x^a y^b=e^m, x^c y^d=e^n, \Delta_1=\left|\begin{array}{ll}m & b \\ n & d\end{array}\right|, \Delta_2=\left|\begin{array}{ll}a & m \\ c & n\end{array}\right|\) and \(\Delta_3=\left|\begin{array}{ll}a & b \\ c & d\end{array}\right|\), then the values of \(x\) and \(y\) are respectively.

1. A \(e^{\frac{\Delta_1}{\Delta_3}}, e^{\frac{\Delta_2}{\Delta_3}}\)
2. B \(e^{\frac{\Delta_3}{\Delta_2}}, e^{\frac{\Delta_1}{\Delta_2}}\)
3. C \(e^{\frac{-\Delta_1}{\Delta_3}}, e^{\frac{-\Delta_2}{\Delta_3}}\)
4. D \(e^{\frac{\Delta_2}{\Delta_1}}, e^{\frac{\Delta_3}{\Delta_1}}\)