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Consider the system of linear equations 5x + 4y - 2z = 2, -2x + 8y - 3z = 6, x + y - 7z = 5. Perform one step Jacobi iteration, using x0 = y0 = z0 = 1 as starting value. Perform one step Gauss-Seidel iteration, using x0 = y0 = z0 = 1 as starting value. Do Jacobi iterations converge for this system? Do Gauss-Seidel iterations converge for this system? Why?

Respuesta :

Answer:

2x-y+3z=1,-3x+4y-5z=0,x+3y-6z=0

Step-by-step explanation:

1. 2x+y+z=5,3x+5y+2z=15,2x+y+4z=8

2. 2x+5y=16,3x+y=11

3. 2x+5y=21,x+2y=8

4. 2x+y=8,x+2y=1

5. 2x+3y-z=5,3x+2y+z=10,x-5y+3z=0

6. x+y+z=3,2x-y-z=3,x-y+z=9

7. x+y+z=7,x+2y+2z=13,x+3y+z=13

8. 2x-y+3z=1,-3x+4y-5z=0,x+3y-6z=0

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