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In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x, X2, . . . , x„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x, – x, = 2 x, + 4x, = 5 3. 2х, x, - 3x, + x3 = -2 -x, + x, - 3rz = -6 5. Apply the Gauss-Seidel method to Exercise 1. 2. – 4x, + 2x, = -6 Зх, - 5х, — %3D 1 = 2 4. 4x, + x, + X3 X2 7 %3D 7x2 + 2x3 - 2 3x, + 4x3 = = 11 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.

In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x, X2, . . . , x„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x, – x, = 2 x, + 4x, = 5 3. 2х, x, - 3x, + x3 = -2 -x, + x, - 3rz = -6 5. Apply the Gauss-Seidel method to Exercise 1. 2. – 4x, + 2x, = -6 Зх, - 5х, — %3D 1 = 2 4. 4x, + x, + X3 X2 7 %3D 7x2 + 2x3 - 2 3x, + 4x3 = = 11 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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 5EQ
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Please answer number 8 gauss sediel method
In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x,, X2, . . . , x„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x, – x, = 2 x, + 4x, = 5 3. 2х, - х, 2. - 4x, + 2x, = -6 Зх, - 5х, — %3D 1 = 2 4. 4x, + x, + X3 7 x, - 3x, + x3 = -2 -x, + x, - 3rz = -6 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. 7x2 + 2x3 - 2 3x, + 4x3 = = 11 8. Apply the Gauss-Seidel method to Exercise 4.
Transcribed Image Text:In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x,, X2, . . . , x„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. 1. 3x, – x, = 2 x, + 4x, = 5 3. 2х, - х, 2. - 4x, + 2x, = -6 Зх, - 5х, — %3D 1 = 2 4. 4x, + x, + X3 7 x, - 3x, + x3 = -2 -x, + x, - 3rz = -6 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. 7x2 + 2x3 - 2 3x, + 4x3 = = 11 8. Apply the Gauss-Seidel method to Exercise 4.
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