Chapter 3.6, Problem 8E

Let Abe an $m\times n$ matrix with $m>n$ . Let $\text{b}\in {\text{R}}^m$ and suppose that $N\left(A\right)=\left\{0\right\}$ .
(a) What can you conclude about the column vectors of A? Are they linearly independent? Do they span ${ℝ}^m$ ? Explain.
(b) How many solutions will the system $A\text{x}=\text{b}$ have if b is not in the column space of A? How many solutions will there be if b is in the column space of A? Explain.