Question

solve the fllowing systems of linear equations by it erative method choose either Jacobi i tre method or Causs- Seidet iterative method i 12x + 3x2 - S X3 = 1 Å4 + 5x2 3x3 =28 3x + 7 Az & 13 43 5 766 use an Inital approximation (x, x xx) = , o, jast conduct at at least fine it eration

Answer 1

Given system of linear equations :

12.01 +3.12 - 5.13 = 1

11 +5.22 + 3.13 = 28

3.01 + 7.02 + 13.13 = 76

The iteration formula for Gauss-Seidel iteration method are :

_x_+1) = 12 12.12" + 12"}

3 (n) .22 (n+1) 2 = = 28 5 1 (n+1) -5-

(n+1) 76 3 7 .(n+1) 76 13 3 (n+1) 1391

COMPUTATION TABLE :

n	x1(n)	x2(n)	x3(n)
0	1	0	1
1	0.5	4.9	3.092307692
2	0.146794871	3.71525641	3.811755424
3	0.742750657	3.164396614	3.970843979
4	0.946752504	3.028143112	3.9971339
5	0.991770013	3.003365657	4.000086951
6	0.999194815	3.000108867	4.000127191
7	1.00002578	2.999918529	4.00003792
8	1.000036168	2.999970015	4.0000078
9	1.000010746	2.999993171	4.000001197
10	1.000002206	2.99999884	4.000000115
11	1.000000338	2.999999863	3.999999996
12	1.000000032	2.999999996	3.999999995
13	0.999999998	3.000000003	3.999999998
14	0.999999998	3.000000001	4
15	0.999999999	3	4
16	0.999999999	3	4
17	1	3	4

Therefore, the solution of the given system is :
X1 = 1
,
X2 = 3
,
X3 = 4
.