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In Exercises 9-12, show that the Gauss-Seidel method diverges for the given system using the initial approximation (x₁, x2,...,x₁) = (0, 0,...,0). 9. X₁ = x₁ - 2x₂1 10. x₁ + 4x₂ = 1

In Exercises 9-12, show that the Gauss-Seidel method diverges for the given system using the initial approximation (x₁, x2,...,x₁) = (0, 0,...,0). 9. X₁ = x₁ - 2x₂1 10. x₁ + 4x₂ = 1

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 25EQ
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Please answer number 9
In Exercises 9-12, show that the Gauss-Seidel method diverges for the given system using the initial approximation (x₁, x₂,..., x₁) = (0, 0, . . . , 0). 9. - - 2x₂ = − 1 X₁ 10. x₁ + 4x₂ = 1 2x₁ + x₂ = 3 3x₁2x₂ = 2 11. 2x₁ - 3x₂ -7 12. x₁ + 3x₂ X1 x3 = 5 - X2 x₁ + 3x₂ 10x3 9 3x₁ - = 5 x₂ + 2x3 = 1 3x1 + = = X3 = 13
Transcribed Image Text:In Exercises 9-12, show that the Gauss-Seidel method diverges for the given system using the initial approximation (x₁, x₂,..., x₁) = (0, 0, . . . , 0). 9. - - 2x₂ = − 1 X₁ 10. x₁ + 4x₂ = 1 2x₁ + x₂ = 3 3x₁2x₂ = 2 11. 2x₁ - 3x₂ -7 12. x₁ + 3x₂ X1 x3 = 5 - X2 x₁ + 3x₂ 10x3 9 3x₁ - = 5 x₂ + 2x3 = 1 3x1 + = = X3 = 13
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