A factory is supplied by an ideal transformer through a short transmission line. At the bus of the factory, a shunt capacitor has been installed to correct its power factor. Which one of the transmission matrices below is correct for this power system?

1) \(\left[\begin{array}{ll}\frac{1}{a} & 0 \\ 0 & a\end{array}ight]\left[\begin{array}{cc}1+\mathbf{Z Y} & \mathbf{Z} \\ \mathbf{Y} & 1\end{array}ight]\)

2) \(\left[\begin{array}{ll}a & 0 \\ 0 & \frac{1}{a}\end{array}ight]\left[\begin{array}{cc}1+\mathbf{Z Y} & \mathbf{Y} \\ \mathbf{Z} & 1\end{array}ight]\)

3) \(\left[\begin{array}{ll}a & 0 \\ 0 & \frac{1}{a}\end{array}ight]\left[\begin{array}{cc}1+\mathbf{Z Y} & \mathbf{Z} \\ \mathbf{Y} & 1\end{array}ight]\)

4) \(\left[\begin{array}{ll}\frac{1}{a} & 0 \\ 0 & a\end{array}ight]\left[\begin{array}{cc}1+\mathbf{Z Y} & \mathbf{Y} \\ \mathbf{Z} & 1\end{array}ight]\)

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