(a) (3 points) Show that finding the optimal estimator by solving the normal equa- tions is equivalent to requiring that the residual vector e = Y - X should average - to zero, and the residual vector e should be orthogonal to X; for every j. That is, show that the matrix form of normal equation can be written as: and n = ei i = 0 n i=1 x e = xi, jei = 0 for all j = 1,..., p. (Hint: Expand the normal equation above and perform matrix multiplication for the first few terms. Can you find a pattern?)