A matrix $M$ is constructed by stacking three column vectors $v_{1}, v_{2}, v_{3}$ as
\[
M=\left[\begin{array}{lll}
v_{1} & v_{2} & v_{3}
\end{array}\right]
\]
Choose the set of vectors from the following options such that $\operatorname{rank}(M)=3$.
$v_{1}=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right], \quad v_{2}=\left[\begin{array}{r}0 \\ -1 \\ 0\end{array}\right], \quad v_{3}=\left[\begin{array}{r}1 \\ -1 \\ 1\end{array}\right]$
$v_{1}=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], \quad v_{2}=\left[\begin{array}{r}-1 \\ 0 \\ 1\end{array}\right], \quad v_{3}=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$
$v_{1}=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right], \quad v_{2}=\left[\begin{array}{r}-1 \\ 0 \\ 1\end{array}\right], \quad v_{3}=\left[\begin{array}{r}1 \\ -1 \\ 1\end{array}\right]$
$v_{1}=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], \quad v_{2}=\left[\begin{array}{r}-1 \\ 1 \\ -1\end{array}\right], \quad v_{3}=\left[\begin{array}{r}0 \\ -1 \\ 0\end{array}\right]$