Let A be an m n matrix with m > n. Let b Rm and

Question:

Let A be an m × n matrix with m > n. Let b ∊ Rm and suppose that N(A) = {0}.
(a) What can you conclude about the column vectors of A? Are they linearly independent? Do they span Rm? Explain.
(b) How many solutions will the system Ax = 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.