Consider the system3x + 7y + 13z = 76x + 5y + 3z = 2812x + 3y - 5z = 1b. Solve the system (as is) using Gauss-Jacobi with initial solution of (x, y, z) = (1,0,1).wwwAnswer:Iteration€1₁%y€al₂%Z12S45€als%

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Answered: Consider the system 3x + 7y + 13z = 76…

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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I+ y - z = -1 Solve the system { 3x + y - z = 7 by reducing into upper triangular form and using back substitution. (5x + 2y – 3z = 3 List all multipliers used and circle all pivots.
Obtain the solution set of the linear equation system given below by using the Jacobi method.Take the initial values 0.NOTE: Proceed only 7 iterations.
Consider the system 3x + 7y + 13z = 76 x + 5y + 3z = 28 12x + 3y - 5z = 1 1. Use any direct method you know to solve for x,y and z. 2. For the Iterative methods, you may use Excel d. Apply the principle of diagonal dominance and solve the system again. Use Gauss-Jacobi with an error tolerance of 0.0001% Answer: Iteration x €₁₁% y €a₂% Z €a₂% 1 2 S 4 Write your observations from the results
Use 3 iterations Use Gauss-Seidel iteration to find the root x3) = (x,(3) X3) of the following system of equations with initial guess X = (0,0,0) 5x,-X2+2x3= 12 3x1+8x2-2x3 = - 25 X1+x2+4X3=6
Part II: Problem Solving. Solve the following: 1. Consider the linear system a. b. 7x + 7 x 2 = 1 Solve the system of linear equations using Jacobi method with L' norm with Tol = 0.001. Show the complete solution for the first 2 iterations. Show your complete table of iterations using the format below. k X1 X2 Δ.x Solve the system of linear equations using Gauss-Seidel method with L² norm with Tol = 0.001. Show the complete solution for the first 2 iterations. Show your complete table of iterations using the format in 1.a.
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Solve the system of linear equations by iteration method (4 iteration). x - 4 y +7 z = 10 5x - 4 y + z = 0 - 4x + 6 y - 4 z = 5 1. X= * X= 1/5(3y-2z) X= 1/5(3y-z) X= 1/5(4y-z) 2. y= * y= 1/6(5+4x-4z) y= 1/6(3y-z) y= 1/5(4y-z) 3. Z= * O z= 1/7(10-x-4y) Z= 1/6(3y-x) Z= 1/5(4y-4x) 4. When first iteration * O X= 0, Y=0.833, Z=1.905 X= 0, Y=1.833, Z=1.905 X= 0, Y=0.833 ,Z=3.905 5. When third iteration * X= 1.295 , Y=0.833, Z=3.241 X= 0, Y=1.833 ,Z=1.905 X= 1.295 , Y=3.495, Z=3.241 O O O O O O O O O
Q2: Use the Gauss-Seidel method to obtain the solution of the system (Two Iteration) 3x1 0.1x - 0.2x3 = 7.85 0. 1x1 + 7x2 - 0.3x3 = -19.3 0. 3x, - 0.2x2 + 10x, 71.4

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Consider the system 3x + 7y + 13z = 76 x + 5y + 3z = 28 12x + 3y - 5z = 1 b. Solve the system (as is) using Gauss-Jacobi with initial solution of (x, y, z) = (1,0,1). www Answer: Iteration €1₁% y €al₂% Z 1 2 S 4 5 €als%