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}.