(b) Given A = 1 4 -1 = 4 1 3 5 02 and b = 4 4 1 (i) Use the Householder transformation to transform A into an upper triangular matrix R. (10) (ii) Apply the same transformation from part (i) to b, that is, compute b() = HHb ((5)) (iii) Solve Rx b() for x and check your answer by computing the residual r = b - Ax'. (3)