5. [More about iterative methods, 5+5+5pt] For x, y E RN, define (x, y) A = a Ay, 1x/A = V(x, x) A where A E RNXN is spd. (a) Show that the above map (., .) A : R x RN - R defines an inner product on RN (b) Consider the linear system Aa* = b with spd A and an approximate solution k E R with residual rk = b - Ack and error ek = a* - Xk. Show that |exl|A = IrkllA-1. (c) Let A E RNXN be spd and bE RN. Define d : RN - R by p(2) = x Ax - bix , TERN. 2 Show that if a* E RN with Ax* = b, then 4(20)