- Why does Theorem G have the title it does?
- Why is Theorem RMRT so surprising ?
- Row-reduce the matrix $A$ to reduced row-echelon form. Without any further computations, compute the dimensions of the four subspaces, (a) $\nsp{A}$, (b) $\csp{A}$, (c) $\rsp{A}$ and (d) $\lns{A}$.
\begin{equation*}
A=
\begin{bmatrix}
1 & -1 & 2 & 8 & 5 \\
1 & 1 & 1 & 4 & -1 \\
0 & 2 & -3 & -8 & -6 \\
2 & 0 & 1 & 8 & 4
\end{bmatrix}
\end{equation*}