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3. 2х, X2 = 2 4. 4x, + х х, — Зх, + х; 3 —2 -x, + x2 - 3xz x – 7x 3x1

3. 2х, X2 = 2 4. 4x, + х х, — Зх, + х; 3 —2 -x, + x2 - 3xz x – 7x 3x1

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 3.
In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x,, x2, . ..,Xx„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. %3D 1. Зх, 2. – 4x, + 2x, = -6 Зх, — 5х, — 5x, = X2 = 2 x + 4x, = 5 1 3. 2х, X2 = 2 4. 4x, + x, + x3 = %3D x - 3x, + x = -2 х, — 7х, + 2х, -2 - + 4x3 -x, + x2 - 3x3 = -6 5. Apply the Gauss-Seidel method to Exercise 1. 3x1 11 %3D = 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.
Transcribed Image Text:In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the initial approximation (x,, x2, . ..,Xx„) = (0, 0, . . . , 0). Continue performing iterations until two successive approximations are identical when rounded to three significant digits. %3D 1. Зх, 2. – 4x, + 2x, = -6 Зх, — 5х, — 5x, = X2 = 2 x + 4x, = 5 1 3. 2х, X2 = 2 4. 4x, + x, + x3 = %3D x - 3x, + x = -2 х, — 7х, + 2х, -2 - + 4x3 -x, + x2 - 3x3 = -6 5. Apply the Gauss-Seidel method to Exercise 1. 3x1 11 %3D = 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.
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