ACT Exam > ACT Questions > Gauss-Seidel method is used to solve the foll...
Start Learning for Free
Gauss-Seidel method is used to solve the following equations (as per the given order):
x1 + 2x2 + 3x3 = 5
2x1 + 3x2 + x3 = 1
3x1 + 2x2 + x3 = 3
Assuming initial guess as x1 = x2 = x3 = 0, the value of x3 after the first iteration is ________
Correct answer is '-6'. Can you explain this answer?
Most Upvoted Answer
Gauss-Seidel method is used to solve the following equations (as per t...
Gauss Seidel Method:
In Gauss Seidel method, the value of x calculated is used in next calculation putting other variable as 0.
x1 + 2x2 + 3x3 = 5
Putting x2 = 0, x3 = 0 ⇒ x1 = 5
2x1 + 3x2 + x3 = 1
Putting x1 = 5, x3 = 0 ⇒ x2 = -3
3x1 + 2x2 + x3 = 3
Putting x1 = 5, x2 = -3 ⇒ x3 = 3 – 3(5) – 2 (-3)
x3 = 3 – 15 + 6
x3 = -6
Mistake Point: Don’t arrange them diagonally because It is given in question solve as per given order.
Free Test
FREE
| Start Free Test |
Community Answer
Gauss-Seidel method is used to solve the following equations (as per t...
Introduction:
The Gauss-Seidel method is an iterative technique used to solve a system of linear equations. It is based on the concept of successive approximations, where each iteration refines the solution until it converges to the desired accuracy. In this problem, we are given a system of three equations and three unknowns, and we need to find the value of x3 after the first iteration using the Gauss-Seidel method.
Given Equations:
The given system of equations is:
1) x1 + 2x2 + 3x3 = 5
2) 2x1 + 3x2 + x3 = 1
3) x1 + 2x2 + x3 = 3
Gauss-Seidel Method:
The Gauss-Seidel method involves solving each equation for one unknown at a time while using the latest approximations for the other unknowns. The process is repeated iteratively until the desired accuracy is achieved.
Initial Guess:
We are given an initial guess of x1 = x2 = x3 = 0.
Iteration 1:
We will substitute the initial guess into the given equations and solve each equation for one unknown at a time.
1) x1 + 2x2 + 3x3 = 5
Substituting x1 = 0, x2 = 0, and x3 = 0:
0 + 2(0) + 3(0) = 0
0 = 5
2) 2x1 + 3x2 + x3 = 1
Substituting x1 = 0, x2 = 0, and x3 = 0:
2(0) + 3(0) + (0) = 0
0 = 1
3) x1 + 2x2 + x3 = 3
Substituting x1 = 0, x2 = 0, and x3 = 0:
0 + 2(0) + (0) = 0
0 = 3
Analysis:
From the above calculations, we can see that the initial guess does not satisfy any of the equations in the system. Therefore, the first iteration does not provide a solution or a refined approximation. The given correct answer of -6 for x3 after the first iteration seems to be incorrect based on the calculations.
Conclusion:
Based on the calculations, the value of x3 after the first iteration cannot be determined as the initial guess does not satisfy any of the equations. The correct answer might be a result of a different method or calculation error.
The Gauss-Seidel method is an iterative technique used to solve a system of linear equations. It is based on the concept of successive approximations, where each iteration refines the solution until it converges to the desired accuracy. In this problem, we are given a system of three equations and three unknowns, and we need to find the value of x3 after the first iteration using the Gauss-Seidel method.
Given Equations:
The given system of equations is:
1) x1 + 2x2 + 3x3 = 5
2) 2x1 + 3x2 + x3 = 1
3) x1 + 2x2 + x3 = 3
Gauss-Seidel Method:
The Gauss-Seidel method involves solving each equation for one unknown at a time while using the latest approximations for the other unknowns. The process is repeated iteratively until the desired accuracy is achieved.
Initial Guess:
We are given an initial guess of x1 = x2 = x3 = 0.
Iteration 1:
We will substitute the initial guess into the given equations and solve each equation for one unknown at a time.
1) x1 + 2x2 + 3x3 = 5
Substituting x1 = 0, x2 = 0, and x3 = 0:
0 + 2(0) + 3(0) = 0
0 = 5
2) 2x1 + 3x2 + x3 = 1
Substituting x1 = 0, x2 = 0, and x3 = 0:
2(0) + 3(0) + (0) = 0
0 = 1
3) x1 + 2x2 + x3 = 3
Substituting x1 = 0, x2 = 0, and x3 = 0:
0 + 2(0) + (0) = 0
0 = 3
Analysis:
From the above calculations, we can see that the initial guess does not satisfy any of the equations in the system. Therefore, the first iteration does not provide a solution or a refined approximation. The given correct answer of -6 for x3 after the first iteration seems to be incorrect based on the calculations.
Conclusion:
Based on the calculations, the value of x3 after the first iteration cannot be determined as the initial guess does not satisfy any of the equations. The correct answer might be a result of a different method or calculation error.
|
Explore Courses for ACT exam
|
|
Similar ACT Doubts
Top Courses for ACTView all
Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer?
Question Description
Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer?.
Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer?.
Solutions for Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT.
Download more important topics, notes, lectures and mock test series for ACT Exam by signing up for free.
Here you can find the meaning of Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer?, a detailed solution for Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? has been provided alongside types of Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Gauss-Seidel method is used to solve the following equations (as per the given order):x1+ 2x2+ 3x3= 52x1+ 3x2+ x3= 13x1+ 2x2+ x3= 3Assuming initial guess as x1= x2= x3= 0, the value of x3after the first iteration is ________Correct answer is '-6'. Can you explain this answer? tests, examples and also practice ACT tests.
|
|
Explore Courses for ACT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup