Q1 For the given equation () = 2 + 2 1: (a) Predict the root using the Newton-Raphson method with initial guess of 0 = 0.5. Compute the root up to the fourth iteration. (8 marks) (b) Predict the root using the The False-Position method with initial guesses of 0 = 0.5 and 1 = 0.5. Compute the root with acceptable level, of 0.5%. (12 marks)

Q2 For the given system and using the LU decomposition method: 3 + 20 = 18 2 3 + 20 = 25 20 + 2 = 17 (a) Find L and U and verify your answers by finding [L][U]. (10 marks) (b) Compute the intermediate vector D. (5 marks) (c) Compute the variables x, y and z. (5 marks)

Q1 For the given equation f(x) = 2e* + 2x - 1: (a) Predict the root using the Newton-Raphson method with initial guess of Xo = 0.5. Compute the root up to the fourth iteration. (8 marks) (b) Predict the root using the The False-Position method with initial guesses of Xo = -0.5 and xz = 0.5. Compute the root with acceptable level, as of 0.5%. (12 marks) Q2 For the given system and using the LU decomposition method: 3x + 20y - z= -18 2x - 3y + 20z = 25 20x + y - 2z = 17 (a) Find L and U and verify your answers by finding [L]X[U]. (10 marks) (b) Compute the intermediate vector D. (5 marks) (c) Compute the variables x, y and z