8. Find the vector a E R" minimizing F(x) = 1QR + Allg - Hallin where Q, H E Rnxn and g E R" are given and A is some parameter that can be tuned for the application. 9. Which of the following subsets of C[a,b] are subspaces? (a) V = {f E C[a, b] : f(a) = f(b) =0} (b) V = {f E C[a, b] : f(a) = f(b) =1} (c) V = {f E C[a, b] : f(a) = 0, f(b) =1} (d) V = {f E C[a, b] : So f (t ) dt = 0} 0. Are the set of solutions to the differential equation d2 a(x) da- 2 u(x) + b(x)- dx u(x) +c(x)u(x) =0, 0