In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x₁, x₂,...,x) = (0, 0,..., 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x₁ x₂ = 2 x₁ + 4x₂ = 5 2. - 4x₁ + 2x₂ = -6 3x₁ - 5x₂ = 1 3. 2x₁ - x₂ 4. 4x₁ + x₂ + x3 7 = x₁ = 3x₂ + x3 = -2 x₁ - 7x₂ + 2x3 2 + 4x3 = = 3x₁ = -x₁ + x₂-3x3 -6 11 5. Apply the Gauss-Seidel method to Exercise 1. 11
In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x₁, x₂,...,x) = (0, 0,..., 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x₁ x₂ = 2 x₁ + 4x₂ = 5 2. - 4x₁ + 2x₂ = -6 3x₁ - 5x₂ = 1 3. 2x₁ - x₂ 4. 4x₁ + x₂ + x3 7 = x₁ = 3x₂ + x3 = -2 x₁ - 7x₂ + 2x3 2 + 4x3 = = 3x₁ = -x₁ + x₂-3x3 -6 11 5. Apply the Gauss-Seidel method to Exercise 1. 11
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer number 5 using gauss sediel method
![In Exercises 1-4, apply the Jacobi method to the given system of
linear equations, using the initial approximation (x₁, x2,...,x₁) =
(0, 0, . . . , 0). Continue performing iterations until two successive
approximations are identical when rounded to three significant digits.
1. 3x₁ x₂ = 2
2. - 4x₁ + 2x₂ = -6
3x₁ - 5x₂ = 1
x₁ + 4x₂ = 5
3. 2x₁ - x₂
2
4. 4x₁ + x₂ + x3
-
x₁ = 3x₂ + x3 = -2
X1
- 7x₂ + 2x3
-x₁ + x₂-3x3 = -6
3x₁
5. Apply the Gauss-Seidel method to Exercise 1.
6. Apply the Gauss-Seidel method to Exercise 2.
7. Apply the Gauss-Seidel method to Exercise 3.
8. Apply the Gauss-Seidel method to Exercise 4.
||
=
=
+ 4x3
7
2
11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2938bd5a-763a-4bd0-9f18-fdc610b49a1b%2F993037fe-2e22-4c40-b6ba-87c69bc3b65f%2Fhuzstuo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 1-4, apply the Jacobi method to the given system of
linear equations, using the initial approximation (x₁, x2,...,x₁) =
(0, 0, . . . , 0). Continue performing iterations until two successive
approximations are identical when rounded to three significant digits.
1. 3x₁ x₂ = 2
2. - 4x₁ + 2x₂ = -6
3x₁ - 5x₂ = 1
x₁ + 4x₂ = 5
3. 2x₁ - x₂
2
4. 4x₁ + x₂ + x3
-
x₁ = 3x₂ + x3 = -2
X1
- 7x₂ + 2x3
-x₁ + x₂-3x3 = -6
3x₁
5. Apply the Gauss-Seidel method to Exercise 1.
6. Apply the Gauss-Seidel method to Exercise 2.
7. Apply the Gauss-Seidel method to Exercise 3.
8. Apply the Gauss-Seidel method to Exercise 4.
||
=
=
+ 4x3
7
2
11
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)