(a) If f(t) = x1e−kt cos(ωt) + x2e−kt sin(ωt), then f0(t) has the same form with coefficients y1,y2. (i) Find the matrix A such that y = Ax. (ii) Find the characteristic polynomial of A. (iii) What can you say about eigenvalues of A? (iv) Interpret your answer to (iii) as a calculus statement. That is, explain how your answer to (iii) could have been predicted from a basic fact of calculus. (b) If f(t) = x1 sin(t) + x2 cos(t) + x3tsin(t) + x4tcos(t), then f0(t) has the same form with coefficients y1,...,y4. Same questions (a)-(d) as previously.