Let $A$ be the matrix below, and find the indicated sets with the requested properties.
\begin{equation*}
A=
\begin{bmatrix}
2 & -1 & 5 & -3\\
-5 & 3 & -12 & 7\\
1 & 1 & 4 & -3
\end{bmatrix}
\end{equation*}
- A linearly independent set $S$ so that $\csp{A}=\spn{S}$ and $S$ is composed of columns of $A$.
- A linearly independent set $S$ so that $\csp{A}=\spn{S}$ and the vectors in $S$ have a nice pattern of zeros and ones at the top of the vectors.
- A linearly independent set $S$ so that $\csp{A}=\spn{S}$ and the vectors in $S$ have a nice pattern of zeros and ones at the bottom of the vectors.
- A linearly independent set $S$ so that $\rsp{A}=\spn{S}$.