Consider the following linear system which may be interpreted as representing a random walker who moves...

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Consider the following linear system which may be interpreted as representing a random walker who moves to the left three times as often as to the right, on a line with positions numbered 0 to 4. When he reaches an end he stops. T₁ = (3/4)xo + (1/4)2 (3/4)x₁+ (1/4)3 23 = (3/4)2 + (1/4) I2 = step length a. Apply the Gauss-Seidel method to the system. Start with the initial approximations (1,0,0,0,0) and compute the third iteration X(0) X (3) b. The system has its exact solution given as Ik = 1- (3-1) (34 - 1)' = k = 0, 1, 2, 3, 4 Compute the exact vector solution X and compare with the results found by the iterative algorithm. Compute the absolute error in l₂ norm. c. Apply SOR method with w = 0.25 to the same system with the same requirement of part a. d. Does under-relaxation (w = 0.25 < 1) in part (c) look promising for the convergen- of this system? Consider the following linear system which may be interpreted as representing a random walker who moves to the left three times as often as to the right, on a line with positions numbered 0 to 4. When he reaches an end he stops. T₁ = (3/4)xo + (1/4)2 (3/4)x₁+ (1/4)3 23 = (3/4)2 + (1/4) I2 = step length a. Apply the Gauss-Seidel method to the system. Start with the initial approximations (1,0,0,0,0) and compute the third iteration X(0) X (3) b. The system has its exact solution given as Ik = 1- (3-1) (34 - 1)' = k = 0, 1, 2, 3, 4 Compute the exact vector solution X and compare with the results found by the iterative algorithm. Compute the absolute error in l₂ norm. c. Apply SOR method with w = 0.25 to the same system with the same requirement of part a. d. Does under-relaxation (w = 0.25 < 1) in part (c) look promising for the convergen- of this system?