Exercise 3.5.26

Choose $d=\mathit{bc}∕a$ to make $\left[\begin{array}{cc}a\hfill & b\hfill \\ c\hfill & d\hfill \end{array}\right]$a rank-1 matrix. Then the row space has basis $(a,b)$ and the nullspace has basis $(-b,a)$. Those two vectors are perpendicular!