Question

4. a) Solve the following equations by Gauss-Seidel method:
10x – 2y – 2z = 6
-x+10y – 2z = 7
-x- y +10z = 8​

Answer 1

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Answer 2

Given : 10x – 2y – 2z = 6

-x+10y – 2z = 7

-x- y +10z = 8​

To Find : Solve for x , y , z

Solution:

10x – 2y – 2z = 6    Eq1

-x+10y – 2z = 7       Eq2

-x- y +10z = 8​         Eq3

Eq1 - Eq2

=> 11x  - 12y  = - 1       Eq4

5*Eq1 + Eq3

=> 49x  -11y  = 38      Eq5

12 * Eq5 - 11 * Eq4

=> 588x  - 121x  =  456 + 11

=>  467x = 467

=> x = 1

=> 11(1) - 12y = - 1

=> y = 1

-x- y +10z = 8​

=> - 1 - 1 + 10z = 8

=> z = 1

x = y = z = 1

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