$A_{1}=A_{1}z\left(1-W\right)\text{ and }A_{1}z\left(1-W\right)=Wz$

$\left\{\begin{matrix}z=\frac{1}{1-W}\text{, }&A_{1}=\frac{W}{1-W}\text{ and }W\neq 1\\z=0\text{, }&A_{1}=0\\z\in \mathrm{R}\text{, }&W=0\text{ and }A_{1}=0\end{matrix}\right.$

$\left\{\begin{matrix}W=\frac{z-1}{z}\text{, }&A_{1}=z-1\text{ and }z\neq 0\\W=0\text{, }&A_{1}=0\\W\in \mathrm{R}\text{, }&A_{1}=0\text{ and }z=0\end{matrix}\right.$