Exercise 3.5.5

$A=\left[\begin{array}{ccc}1\hfill & 1\hfill & 1\hfill \\ 2\hfill & 1\hfill & 0\hfill \end{array}\right]$has those rows spanning its row space. $B=\left[\begin{array}{ccc}1\hfill & -2\hfill & 1\hfill \end{array}\right]$ has the same rows spanning its nullspace and $A{B}^T=0$.