(b) Given A = 1 4 -1 = 4 1 3 5 02 and b =...

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(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(¹) = H₂H₁b ((5)) (iii) Solve Rx b(¹) for x and check your answer by computing the residual r = b - Ax'. (3) (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(¹) = H₂H₁b ((5)) (iii) Solve Rx b(¹) for x and check your answer by computing the residual r = b - Ax'. (3)