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For the set of linear equations given below, what is the value of voltage V1 after first iteration of Gauss Siedal method? Assume the initial approximation is V1 = 0
10V1 + 2V2 = 10, 4V1 + 7V2 = 15
10V1 + 2V2 = 10, 4V1 + 7V2 = 15
- a)1
- b)0.5714
- c)0.5
- d)0.6367
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
For the set of linear equations given below, what is the value of volt...
The given equations can be written as
10V1 + 2V2 = 10
⇒ V1 = 1/10 [10 − 2V2]
4V1 + 7V2 = 15
⇒ V2 = 1/7 [15 − 4V1]
Iteration 1:
Put V2 = 0
⇒ V1 = 1/10 [10 − 0] = 1
10V1 + 2V2 = 10
⇒ V1 = 1/10 [10 − 2V2]
4V1 + 7V2 = 15
⇒ V2 = 1/7 [15 − 4V1]
Iteration 1:
Put V2 = 0
⇒ V1 = 1/10 [10 − 0] = 1
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For the set of linear equations given below, what is the value of volt...
Overview of the Gauss-Seidel Method
The Gauss-Seidel method is an iterative technique to solve linear systems. It updates the variables one at a time using the latest values.
Given Equations
The system of equations we have is:
1. 10V1 + 2V2 = 10
2. 4V1 + 7V2 = 15
Initial Conditions
- First iteration starts with V1 = 0 and V2 = 0.
Calculating V1 in the First Iteration
1. From the first equation:
10V1 + 2V2 = 10
Substituting the initial values:
10(0) + 2(0) = 10 → 0 = 10 (not useful)
2. Rearranging for V1:
V1 = (10 - 2V2) / 10
Substituting V2 = 0:
V1 = (10 - 2(0)) / 10
V1 = 10 / 10
V1 = 1
Updating V2 in the First Iteration
1. Now use V1 = 1 to find V2:
From the second equation:
4V1 + 7V2 = 15
4(1) + 7V2 = 15
4 + 7V2 = 15
7V2 = 15 - 4
7V2 = 11
V2 = 11/7 ≈ 1.5714
Conclusion
After the first iteration, the value of V1 is indeed 1. Therefore, the correct option is:
Option 'A': 1
The Gauss-Seidel method is an iterative technique to solve linear systems. It updates the variables one at a time using the latest values.
Given Equations
The system of equations we have is:
1. 10V1 + 2V2 = 10
2. 4V1 + 7V2 = 15
Initial Conditions
- First iteration starts with V1 = 0 and V2 = 0.
Calculating V1 in the First Iteration
1. From the first equation:
10V1 + 2V2 = 10
Substituting the initial values:
10(0) + 2(0) = 10 → 0 = 10 (not useful)
2. Rearranging for V1:
V1 = (10 - 2V2) / 10
Substituting V2 = 0:
V1 = (10 - 2(0)) / 10
V1 = 10 / 10
V1 = 1
Updating V2 in the First Iteration
1. Now use V1 = 1 to find V2:
From the second equation:
4V1 + 7V2 = 15
4(1) + 7V2 = 15
4 + 7V2 = 15
7V2 = 15 - 4
7V2 = 11
V2 = 11/7 ≈ 1.5714
Conclusion
After the first iteration, the value of V1 is indeed 1. Therefore, the correct option is:
Option 'A': 1
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For the set of linear equations given below, what is the value of voltage V1 after first iteration of Gauss Siedal method? Assume the initial approximation is V1 = 010V1 + 2V2 = 10, 4V1 + 7V2 = 15a)1b)0.5714c)0.5d)0.6367Correct answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about For the set of linear equations given below, what is the value of voltage V1 after first iteration of Gauss Siedal method? Assume the initial approximation is V1 = 010V1 + 2V2 = 10, 4V1 + 7V2 = 15a)1b)0.5714c)0.5d)0.6367Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the set of linear equations given below, what is the value of voltage V1 after first iteration of Gauss Siedal method? Assume the initial approximation is V1 = 010V1 + 2V2 = 10, 4V1 + 7V2 = 15a)1b)0.5714c)0.5d)0.6367Correct answer is option 'A'. Can you explain this answer?.
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