ANSWER 3,4,5,6

. Let A : [ _i _i :; ] . Find a vector 3*: in N{A) and verify that it is orthogonal to the rows of A. 2 l i Let ml 2 U ,a2 = 1 . Find a unit vector 2% that is orthogonal to both (11 and a2. 1 ,1 1 2 l .Leta= 3 ,b= 6 ,c= U 1 2 1 (a Show that b is parallel to a; and c is perpendicular to a. (b ) ) Find P, the projection matrix onto 3, the span of a. (c) Find projsaj and projs(c). ) (a Find the equation of the straight line which best fits the following points (1= 1), (2, 3), (4,6), and ('5: 5)- 3be (b) Let A : . Find P, the projection matrix on C(A). hllih'ri 5 . Find the equation of the straight line which best ts the following points (0, 1), (1,2), and (2, 1). Comment on the result. (a) Find the equation of the straight line 1,: : so + alt which best ts the following points (thug): (1,3), (2,4), and (3,415). (b) Calculate the error e = [r31 82 B3JT, where 8% 2 hi (a0 + mtg); and show that e is perpendicular to C(A)