For each of the following state whether the statements are true or false and give a reason in each case.
(a) If F : R^n → R^m is a linear transformation and n > m then there exists a nonzero vector x such that F (x) = 0.
(b) If F : R^n → R^m and G : R^k → R^n are linear transformations such that ker F = {0} and ker G = {0} then ker F ? G = {0}.