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, . . . , O). 21. -4x, + 5x, = 1 22. 4.x, + 2.x, - 2.x, = 0 X, - 3x, - x, = 7 3x, - x2 + 4.x, = 5 X, + 2x, = 3
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, . . . , O). 21. -4x, + 5x, = 1 22. 4.x, + 2.x, - 2.x, = 0 X, - 3x, - x, = 7 3x, - x2 + 4.x, = 5 X, + 2x, = 3
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 50EQ
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Please answer number 21 with complete solution.
![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%2F41663cc2-cd7b-4283-ad17-a0f6181c7966%2Fpon8xc_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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