(Solved): 7. (6 pts) Determine if the set \( S \) of vectors is linearly independent, or linearly dependent ...

7. (6 pts) Determine if the set \( S \) of vectors is linearly independent, or linearly dependent by row reducing appropriate matrix. If the set is linearly dependent, provide a non trivial solution to \( c_{1} \vec{v}_{1}+\cdots+c_{k} \vec{v}_{k}=\overrightarrow{0} \). \[ S=\left\{\left[\begin{array}{l} 1 \\ 6 \\ 3 \end{array}\right],\left[\begin{array}{c} -5 \\ 3 \\ -9 \end{array}\right],\left[\begin{array}{c} -1 \\ 5 \\ -1 \end{array}\right]\right\} \]