Consider a differential equation x = Ax + b(t) (*) with x ER" and b: R Rn continuous and of period 7 > 0, that is, b(t + 7) = b(t) for some 7 > 0. (a) Assume the following condition on the matrix A holds: XT If A is an eigenvalue of A then is not an integer. 2i Prove that equation (*) has a unique solution of period 7. (**) (b) Prove that if (**) is false then there exists some b(t) as above such that equation (*) does not have a T-periodic solution.