已知实数三阶方阵 $A$ 满足 $A\left[\begin{array}{l}1 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{c}0 \\ -1 \\ 1\end{array}\right], A\left[\begin{array}{r}0 \\ -1 \\ 1\end{array}\right]=\left[\begin{array}{l}1 \\ 1 \\ 0\end{array}\right], A\left[\begin{array}{c}1 \\ 0 \\ -1\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$ 。试问有多少个行向量 $\vec{v}=\left[\begin{array}{l}v_1 \\ v_2 \\ v_3\end{array}\right]$ 满足 $A \vec{v}=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right]$ 且 $\vec{v}$ 垂直於行向量 $\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]$ ？