ANSWER ONLY (iii) and (iv) Round off to 3 decimal placeThe 3x3 system below has solutions x₁=1,x₂ = -2 and X₂=04x₁+2x₂=2x3 = 02x₁-6x2 - 2x3 = 143X₁-X₂ +4X3 = 5(1) Explain why this system is not quickly strictlydiagonally dominant (hereafter 5DD)(i) Using the initial approximation X₁0 = 0.75, X₁² = -1.75and X300) = -0.35, apply three iterations of the JacobiMethod to the above system208.(0)(0)(iii) Taking the initial approximation X₂₁ =0.75, X₂ = -1.75and x300) = -0.35, apply three iterations of theJacobi Method to the above system(iv) Will the Jacobi and Gauss-Siedel iterates For all 3x3linear systems that are not SDD always eliverge?If not, give an example of a system that is not SDD,but for which the Jacobi and Grauss- Siedel iteratesconverge to the solution of the system.

Answered: Image /qna-images/answer/2e9bd2ea-00fa-417c-86a2-8112d637e355.jpg

Round off to 3 decimal place The 3x3 system below has solutions x₁=1, Xa=-2 and x3 = 4x+2x2-2x3 = 0 2x1-6x2 - 2x3 = 14 3X₁-X₂ +4X3 = 5 i Explain why this system is not quickly strictly diagonally dominant (hereafter 5DD) -(0) (iu) Using the initial approximation X₁0 =0.75, X = -1.75 and x3 = -0.35, apply three iterations of the Jacobi Method to the above system (0) () (iii) Taking the initial approximation X₁₂ =0.75, X₂ = -1.75 and x300) = -0.35, apply three iterattiers of the Jacobi Method to the above system (iv) Will the Jacobi and Grauss-Siedel iterates For all 3x3 linear systems that are not SDD always eliverge? If not, give an example of a system that is not SDD. but for which the Jacobi and Grauss- Siedel iterates converge to the solution of the system.

Round off to 3 decimal place The 3x3 system below has solutions x₁=1, Xa=-2 and x3 = 4x+2x2-2x3 = 0 2x1-6x2 - 2x3 = 14 3X₁-X₂ +4X3 = 5 i Explain why this system is not quickly strictly diagonally dominant (hereafter 5DD) -(0) (iu) Using the initial approximation X₁0 =0.75, X = -1.75 and x3 = -0.35, apply three iterations of the Jacobi Method to the above system (0) () (iii) Taking the initial approximation X₁₂ =0.75, X₂ = -1.75 and x300) = -0.35, apply three iterattiers of the Jacobi Method to the above system (iv) Will the Jacobi and Grauss-Siedel iterates For all 3x3 linear systems that are not SDD always eliverge? If not, give an example of a system that is not SDD. but for which the Jacobi and Grauss- Siedel iterates converge to the solution of the system.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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