The set does span all of \(\mathbb{R}^{ 3 }\).

Vectors:
\[
\begin{bmatrix} 
 2  \\ 
 -2  \\ 
 -1
\end{bmatrix} \quad \begin{bmatrix} 
 3  \\ 
 0  \\ 
 -1
\end{bmatrix} \quad \begin{bmatrix} 
 -1  \\ 
 4  \\ 
 1
\end{bmatrix} \quad \begin{bmatrix} 
 4  \\ 
 -1  \\ 
 -1
\end{bmatrix} \quad 
\]
        

The set does span all of \(\mathbb{R}^{ 3 }\).