Choose solution set $S$ corresponding to the systems of two equations
$$\begin{array}{r}
x-2 y+z=0 \\
x-z=0
\end{array}$$
Note: $\mathscr{R}$ denotes the set of real numbers
- $S=\left\{\alpha\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right) \mid \alpha \in \mathscr{R}\right\}$
- $S=\left\{\alpha\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)+\beta\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right) \mid \alpha, \beta \in \Re\right\}$
- $S=\left\{\alpha\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)+\beta\left(\begin{array}{l}2 \\ 1 \\ 2\end{array}\right) \mid \alpha, \beta \in \Re\right\}$
- $S=\left\{\alpha\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right) \mid \alpha \in \mathscr{R}\right\}$