For the diagonally dominant systems in Exercise 10.5.3. starting with the initial guess x = y = z = 0, compute the solution to 3 decimal places using the Gauss-Seidel method. Check your answer by solving the system directly by Gaussian Elimination.
In Exercise 10.5.3
Which of the following systems have a diagonally dominant coefficient matrix?
(a) 5x - y = 1
-x + 3y = - 1
(b) 1/2 x + 1/3 y = 1
1/5 x + 1/4 y = 6
(c) -5x + y = 3
-3x + 2y = -2
(d) -2x + y + z = 1
-x + 2y - z = -2
x - y + 3 z = 1
(e) - x + 1/2 y + 1/3 z = 1
1/3 x + 2y + 3/4 z = -3
2/3 x 1/4 y - 3/2 z = 2
(f) x - 2y + z = 1
-x + 2y + z = -1
x + 3y - 2z = 3
(g) - 4x + 2y + z = 2
-x + 3y + z = -1
x + 4y - 6z = 3