Consider the n-dimensional linear time-invariant system x = Ax+u(t), where v is an eigenvector of A. x(0) =V, t≥ 0, (a) Assume that u(t) = 0, Vt≥0. Show that the solution to the initial value problem (1) can be written as x(t) = a(t)v, Vt ≥ 0, where a(t) is scalar function of time. Hint: try to determine what a(t) needs to be by substituting the candidate x(t) in the differential equation. (b) Show that when u(t) = etv, t≥ 0 the solution to the initial value problem (1) is also aligned with v (i.e., can also be written as a scalar function times v).