1. (30 marks total) Consider the 2 x 2 matrix = [=38]. Answer the following questions: (a) (8 marks) Determine the (i) characteristic polynomial and (ii) the eigenvalues of A. (b) (8 marks) Determine the eigenvectors corresponding to each eigenvalue. (c) (14 marks) Let eat = eat (Bcos(bt) + Csin(bt)), determine the scalars a, b and the real 2 x 2 matrices B and C. (Hint: Use the Euler identities cos(x) = (elf + e-#7) /2 and sin(x) = (el - e -7) / (2j), 3 = V-1)