Exercise 3.3 [Gauss-Jocobi method & Gauss-Seidel method]

EXERCISE 3.3 [Gauss-Jocobi method & Gauss-Seidel method]

Solve, the following system of equations by using Gauss-Jacobi and Gauss-Seidel method.

1. 8x - 3y + 2z = 20, 4x + 11y – z = 33, 6x + 3y + 12z = 35.

[Ans. 3.0168, 1.9859, 0.9118]

[A.U CBT N/D 2011, A.U M/J 2012] -

2. 5x - 2y + z = -4, x + 6y - 2z = -1, 3x + y + 5z = 13[A.U N/D 2015 R13 SNM]

[Ans. -1.001, 0.999, 3]

3. 30x - 2y + 3z = 75, 2x + 2y + 18z = 30, x + 17y - 2z = 48

 [Ans. 2.5796, 2.7976, 1.0692] [AU M/J 2016 R13 SNM, N/D 2019 R-13]

4. 10x - 2y + z = 12, x + 9y - z = 10, 2x - y + 11z = 20

[Ans. 1.2624, 1.1591, 1.6940]

5. 2x + y + z = 4, x + 2y + z = 4, x + y + 2z = 4

[Ans. 1, 1, 1]

6. 7.6x - 2.4y + 1.3z = 20.396, 3.7x + 7.9y - 2.5z = 35.866 1.9x - 4.3y + 8.2z = 32.514

 [Ans. 3.23, 4.85, 5.76]

7. x - 2y +10z = 30.6, 2x + 5y - z = 10.5, 3x + y + z = 9.3

[Ans. 1.2, 2.3, 3.4]

8. 8x – y + z = 18, 2x + 5y - 2z = 3, x + y - 3z = -16

[Ans. 1.7297, 2.6216, 6.7838]

9. 83x + 11y - 4z = 95, 7x + 52y + 13z = 104, 3x + 8y + 29z = 71

 [Ans. 1.06, 1.37, 1.96]

10. 10x - 2y - z-t = 3, -2x + 10y - z -t =15, -x - y + 10z – 2t = 27, 28 50 – x – y -22 + 10t = -9

 [Ans. 0, 1, 2, 3]

11. 9x₁ + 2x₂ + 4x₃ = 20, x₁ + 10x₂ + 4x₃ = 6, 2x₁ - 4x₂ + 10x₂ = -15

[Ans. x₁ = 2.737, x₂ = 0.987, x₃ = -1.653]

12. 1.02x₁ -0.05x₂ - 0.10x₃ = 0.795

- 0.11x₁ + 1.03x₂  - 0.05x₃ = 0.849

- 0.11x₁ - 0.12x₂ + 1.04x₃ = 1.398

 [Ans. x₁ = 0.982, x₂ = 1.005, x₃ = 1.564]

13. 6x₁ – x₂ – x₃ = 11.33, - x₁ + 6x₂ – x₃ = 32, - x₁ – x₂ + 6x₃ = 42

[Ans. x₁ = 4.666, x₂ = 7.619, x₃ = 9.048]

14. 8x + y + z = 8, 2x + 4y + z = 4, x + 3y + 5z = 5

[Ans : x = 0.876, y = 0.419, z = 0.574]

15. 28x + 4y - z 32, x + 3y + 10z = 24, 2x + 17y + 4z = 35

 [Ans. x = 0.9936, y = 1.507, z = 1.8486]

 [A.U Tvli M/J 2010] [A.U CBT A/J 2011] [A.U N/D 2016 R13 SNM] Jarreo e [A.U N/D 2017 R-13]

16. y - x + 10z = 35.61, x + z + 10y = 20.08, y z + 10x = 11.19

[Ans. x = 1.321, y = 1.522, z = 3.541]

17. 4x + 2y + z = 14, x + 5y - z = 10, x + y + 8z = 20

[Ans. x = 2, y = 2, z = 2]

18. 20x + y - 2z = 17, 3x + 20y – z - 18, 2x - 3y + 20z = 25

 [Ans. x = 1, y = -1, z = 1]

[A.U M/J 2009, N/D 2009]

[A.U M/J 2012, N/D 2014] [A.U M/J 2016 R13]