In Exercises 21 and 22, the coefficient matrix of the system of linear equations is not strictly diagonally dominant. Show that the Jacobi and Gauss-Seidel methods converge using an initial approximation of (x,, x2, . . . , x,) = (0, 0, . . . , 0). 21. -4x, + 5x, = 1 22. 4.x, + 2.x, - 2.x, = 0 X - 3x, - x, = 7 3x1 *, + 2x, = 3 X2 + 4.x, = 5
In Exercises 21 and 22, the coefficient matrix of the system of linear equations is not strictly diagonally dominant. Show that the Jacobi and Gauss-Seidel methods converge using an initial approximation of (x,, x2, . . . , x,) = (0, 0, . . . , 0). 21. -4x, + 5x, = 1 22. 4.x, + 2.x, - 2.x, = 0 X - 3x, - x, = 7 3x1 *, + 2x, = 3 X2 + 4.x, = 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PLEASE ANSWER NUMBER 21 MATH 221 : PLEASE GIVE DETAILED SOLUTIONS AND CORRECT ANSWERS. I WILL REPORT TO BARTLEBY THOSE TUTORS WHO WILL GIVE INCORRECT ANSWERS.
![In Exercises 21 and 22, the coefficient matrix of the system of linear
equations is not strictly diagonally dominant. Show that the Jacobi
and Gauss-Seidel methods converge using an initial approximation
of (x1, x2, . . . , x,) = (0, 0, . . . , 0).
21. -4x, + 5x, = 1
X, + 2x, = 3
22. 4.x, + 2x, - 2.x, = 0
X, - 3x, - x, = 7
3x, - x2 + 4.x, = 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F745d5e84-61e0-4513-9d33-8b169b19b6a1%2F4443d0e8-0116-453b-92cc-7283ec4d138c%2Fss5kz5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 21 and 22, the coefficient matrix of the system of linear
equations is not strictly diagonally dominant. Show that the Jacobi
and Gauss-Seidel methods converge using an initial approximation
of (x1, x2, . . . , x,) = (0, 0, . . . , 0).
21. -4x, + 5x, = 1
X, + 2x, = 3
22. 4.x, + 2x, - 2.x, = 0
X, - 3x, - x, = 7
3x, - x2 + 4.x, = 5
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