Which of the following is(are) sufficient argument(s) to show that the vectors of set $\text{S}$ are linearly dependent?
$$
\text{S}=\left\{u=\left[\begin{array}{c}
1 \\
-2 \\
7
\end{array}\right], v=\left[\begin{array}{c}
-7 \\
14 \\
-49
\end{array}\right], w=\left[\begin{array}{l}
0 \\
0 \\
0
\end{array}\right]\right\}
$$
Treat each option independently, correct option independently should be sufficient to infer that vectors are linearly dependent.
- $0 u+0 v+1 w=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$
- $0 u+0 v=w$
- $0 u+0 v+0 w=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$
- $7 u+(-1) v+1 w=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$
