Consider the subset $W$ below as a candidate for being a subspace of $\complex{2}$ \begin{equation*} W=\setparts{\colvector{x_1\\x_2}}{3x_1-5x_2=12} \end{equation*}
The zero vector of $\complex{2}$, $\zerovector=\colvector{0\\0}$ will need to be the zero vector in $W$ also. However, $\zerovector\not\in W$ since $3(0)-5(0)=0\neq 12$. So $W$ has no zero vector and fails Property Z of Definition VS. This subspace also fails to be closed under addition and scalar multiplication. Can you find examples of this?