Answer #1Handwritten then box the final answer 1. () Use the Jacobi method and Gauss-Seidel method to solve the following system until the 7.¹-norm ofAx is less than or equal to Tol = 1 x 10-4. Show the detailed calculation of the first 3 iterations.2.10x₁ + 2x₂x₂ = 27x₁ + x₂ + 5x3 = -21.5-3x₁6x₂ + 2x3 = -61.5Use the Jacobi method and Gauss-Seidel method to solve the following system until L²-norm of Ax isless than or equal to Tol = 1 x 10-4. Show the detailed calculation of the first 3 iterations.-4c₁-₁₂ + 12c₂ = 235015c₁3c₂-c3 = 3800-3c₁ + 18c-6c₁ = 12003. () Use the Relaxation method to solve the following system until the 1.0-norm of Ax is less than or equalto Tol = 0.001. Use = (a) 0.95 and (b) 1.20. Show the detailed calculation of the first 3 iterations.18-01 26 -21-2 7 2

Answered: Image /qna-images/answer/82d9df7f-38aa-40b8-9a01-0bb2346f6a95.jpg

Answered: ) Use the Jacobi method and…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 60EQ

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Apply the Gauss-Seidel Method to solve the linear system below with precision ε = 0.001. Consider as stopping criterion max1 ≤ i ≤ 3 |xki −x(k−1)i|<0.001 and, as initial approximation, x01=−5.6,x02=−2.5 ,x03=1.3 . Fill in the table below with the approximations obtained at each iteration of the method, until obtaining the established precision or until calculating 5 iterations. Leave the remaining rows with a value of 0 in all columns. Note that iteration 0 is already populated. Perform calculations with 4 decimal places and rounding. Use comma as separator for fractional values (Ex: 3.145 instead of 3.145).

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) Use the Jacobi method and Gauss-Seidel method to solve the following system until the 1.¹-norm of 1. ( Ax is less than or equal to Tol = 1x 10. Show the detailed calculation of the first 3 iterations. 10x₁ + 2x₂x₂ = 27 x₁ + x₂ + 5x3 = -21.5 -3x₁-6x₂ + 2x3 = -61.5