8. Let $A$ be a 5 by 7 matrix with rank 4.

(a) (5%) What is the dimension of the solution space of $A\mathbf{x} = \mathbf{0}$?

(b) (5%) Is $A\mathbf{x} = \mathbf{b}$ consistent for all vectors $\mathbf{b}$ in $\mathbb{R}^5$? Explain.