(a)Suppose A is an m×n matrix with linearly independent columns, and suppose there is a vector b ∈ Rm for which the equation Ax = b does not have a solution.
Show that m > n. (Hint: One approach "proof by contradiction," i.e., what if m ≤ n?)
(b) Suppose A is an m×n matrix and that the equation Ax = b is consistent for all b ∈ Rm, and suppose that the columns of A are linearly dependent.
Then m = n