$\text{rank}(A) = 1$, $\text{nullity}(A) = 2$

$\text{rank}(A) = 2$, $\text{nullity}(A) = 1$

$\text{rank}(A) = 3$, $\text{nullity}(A) = 0$

$\text{rank}(A) = 0$, $\text{nullity}(A) = 3$