Exercise 4.1.21

For example $(-5,0,1,1)$ and $(0,1,-1,0)$ span $S^{\text{⊥}}=$ nullspace of $A=\left[\begin{array}{cccc}1\hfill & 2\hfill & 2\hfill & 3\hfill \\ 1\hfill & 3\hfill & 3\hfill & 2\hfill \end{array}\right]$.