$\mathbf{b} \in \text{Col}(A)$ because $A\mathbf{x} = \mathbf{b}$ is consistent

$\mathbf{b} \notin \text{Col}(A)$ because the system is inconsistent

$\mathbf{b}$ is always in $\text{Col}(A)$ for any $\mathbf{b}$

Cannot determine without computing the full column space