Question

2. (20 pts. Consider a set of equations 4.x - x - x = 3 - 2x + 6x2 + x3 = 9 -X, + x + 7x, = -6 Find X, X., and x, by using Gauss-Seidel method (no credit will be given for other methods) with an initial estimation (x,x,x)=(0,0,0) Note: Use the table below for 4 steps with 3 decimal places, k 0 1 0 0 0 2 3 4

Answer 1

4x1 - x - x2 = 3 -2x1 + 6x2 + x3 =p 22 +7x3 = -6 Seidel method We Gauss gd iterative formula by (kzo) (R+1) [3+ xolk) x3 (6) 4 (k+1) ( 9 + 27,1 kv) (k) X3 X2 -14 (6+1) 23 (R+1) (R+1) 72 [-6 + - *+] - initial xco, (x,10), x) Xylo)) 10,o, o)

Table 13 decimal place) 306) = (2,4), x,K), *) (steration) k (k) () X2 (k) O 0 0 (Given) 1 0.75 1.75 -1 ( Rut kio) 9n 2 0.938 1.979 -1.006 (Put k=1) abou Iterative formula 3 0.993 1.999 -1.ool (Put ka 2) 4 0.9995 2 - ) (lut k-3) - 1 X₂ = 2 Xz =
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