Exercise 4.1.33

Both $r$ ’s must be orthogonal to both $n$ ’s, both $c$ ’s must be orthogonal to both $\ell$ ’s, each pair ( $r$ ’s, $n$ ’s, $c$ ’s, and $\ell$ ’s) must be independent. Fact: All $A$ ’s with these subspaces have the form $\left[c_1{c}_2\right]M{\left[r_1{r}_2\right]}^T$ for a 2 by 2 invertible $M$.

You must take $\left[c_1,c_2\right]$ times ${\left[r_1,r_2\right]}^T$.