Exercise 1.3.8

We have $A=\left[\begin{array}{cc}\hfill 0\hfill & \hfill 1\hfill \\ \hfill 0\hfill & \hfill 0\hfill \end{array}\right]$, it’s easy to see that $C=\left[\begin{array}{c}\hfill 1\hfill \\ \hfill 0\hfill \end{array}\right]$ and let $\mathit{Ax}=0$, and solve for $x$, we have $x=\left[\begin{array}{c}\hfill c\hfill \\ \hfill 0\hfill \end{array}\right]$, where $c$ is any number. It’s clear that the column space and nullspace are the same in such case.