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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 x₁ + 4x₂ = 5 3x₁ - 5x₂ = 1 3. 2x₁ - x₂ = x2 2 4. 4x₁ + x₂ + x3 1 = x₁ = 3x₂ + x3 = -2 X1 7x₂ + 2x3 = + 4x3 - -x₁ + x₂ = 3x3 = -6 3x₁ = 5. Apply the Gauss-Seidel method to Exercise 1. 6. Apply the Gauss-Seidel method to Exercise 2. 7 2 11

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 x₁ + 4x₂ = 5 3x₁ - 5x₂ = 1 3. 2x₁ - x₂ = x2 2 4. 4x₁ + x₂ + x3 1 = x₁ = 3x₂ + x3 = -2 X1 7x₂ + 2x3 = + 4x3 - -x₁ + x₂ = 3x3 = -6 3x₁ = 5. Apply the Gauss-Seidel method to Exercise 1. 6. Apply the Gauss-Seidel method to Exercise 2. 7 2 11

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 6EQ
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Please answer number 6. Rounded it to 3 significant digits.
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
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
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