GATE ME 2016 Set 1 — Question 39
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Engineering Mathematics → Numerical Methods → Gauss, Jacobi & Gauss-Seidel
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Question
Gauss-Seidel method is used to solve the following equations (as per the given order):
Assuming initial guess as , the value of after the first iteration is ________
Assuming initial guess as , the value of after the first iteration is ________
Correct answer
-6
Solution
The given system of equations is:
1)
2)
3) For the Gauss-Seidel method, we rearrange each equation to solve for one variable:
The initial guess is .Now, we perform the first iteration:Calculate using and :
Calculate using the updated and :
Calculate using the updated and :
So, the value of after the first iteration is .
1)
2)
3) For the Gauss-Seidel method, we rearrange each equation to solve for one variable:
The initial guess is .Now, we perform the first iteration:Calculate using and :
Calculate using the updated and :
Calculate using the updated and :
So, the value of after the first iteration is .
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