Exercise 4.1.11

For $A$ : The nullspace is spanned by $(-2,1)$, the row space is spanned by $(1,2)$. The column space is the line through $(1,3)$ and $N\left(A^T\right)$ is the perpendicular line through $(3,-1)$. For $B$ : The nullspace of $B$ is spanned by $(0,1)$, the row space is spanned by $(1,0)$. The column space and left nullspace are the same as for $A$.