j4=matrix1111^T

Let x1 =j4, X2 = (4,1, 3, 4), y = (1,9,5,5). Let V = L(x1,x2). a. Find = P(y|V) and e=y-. b. Find =p(y|x) and 2 = p(y|x2) and show that #i +2. c. Verify that elv. d. Find ||y|12, ll||, ||ell, and verify that the Pythagorean Theorem holds. Compute |||2 directly from and also by using the formula ll||2 = y Py where P is the projection matrix onto V. e. Use Gram-Schmidt orthogonalization to find four mutually orthogonal vec- tors V1, V2, V3, and VA such that V = L(v1,v2). Hint: You can choose x3 and x4 arbitrarily, as long as X1, X2, X3, XA are LIN