Consider A ∈ Mat3×3(R) and the vector v ∈R3 such that A3v = 0, but A2v 6= 0, (a) Show that the vectors A2v, Av, and v form a basis of R3. Hint: It is sufficient to show they are linearly independent. Set up the proper equation, and multiply by A2. (b) Find the matrix of the transformation T(x) = Ax with respect to the basis {A2v, Av, v}.

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem