The set does not span all of \(\mathbb{R}^{ 3 }\).

Vectors:
\[
\begin{bmatrix} 
 0  \\ 
 6  \\ 
 0
\end{bmatrix} \quad \begin{bmatrix} 
 2  \\ 
 4  \\ 
 -2
\end{bmatrix} \quad \begin{bmatrix} 
 -2  \\ 
 -22  \\ 
 2
\end{bmatrix} \quad \begin{bmatrix} 
 -8  \\ 
 -34  \\ 
 8
\end{bmatrix} \quad 
\]
        

The set does not span all of \(\mathbb{R}^{ 3 }\).