Let $A$ be the matrix below.
- Find a set $S$ so that $\nsp{A}=\spn{S}$.
- If $\vect{z}=\colvector{3 \\ -5 \\ 1 \\ 2}$, then show directly that $\vect{z}\in\nsp{A}$.
- Write $\vect{z}$ as a linear combination of the vectors in $S$.
\begin{align*}
A=
\begin{bmatrix}
2 & 3 & 1 & 4 \\
1 & 2 & 1 & 3 \\
-1 & 0 & 1 & 1
\end{bmatrix}
\end{align*}