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6. Gauss Jacobi method example ( Enter your problem )
  1. Example `2x+5y=21,x+2y=8`
  2. Example `2x+5y=16,3x+y=11`
  3. Example `x+y+z=3,2x-y-z=3,x-y+z=9`
  4. Example `x+y+z=7,x+2y+2z=13,x+3y+z=13`
Other related methods
  1. Inverse Matrix method
  2. Cramer's Rule method
  3. Gauss-Jordan Elimination method
  4. Gauss Elimination Back Substitution method
  5. Gauss Seidel method
  6. Gauss Jacobi method
  7. Elimination method
  8. LU decomposition using Gauss Elimination method
  9. LU decomposition using Doolittle's method
  10. LU decomposition using Crout's method
  11. Cholesky decomposition method
  12. SOR (Successive over-relaxation) method
  13. Relaxation method

1. Example `2x+5y=21,x+2y=8`
(Previous example)
3. Example `x+y+z=3,2x-y-z=3,x-y+z=9`
(Next example)

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





Solve Equations 2x+5y=16,3x+y=11 using Gauss Jacobi method

Solution:
Total Equations are `2`

`2x+5y=16`

`3x+y=11`


The coefficient matrix of the given system is not diagonally dominant.
Hence, we re-arrange the equations as follows, such that the elements in the coefficient matrix are diagonally dominant.
`3x+y=11`

`2x+5y=16`


From the above equations
`x=1/3(11-y)`

`y=1/5(16-2x)`

Solution steps are
`1^(st)` Approximation

`x_1=1/3[11-(0)]=1/3[11]=3.666667`

`y_1=1/5[16-2(0)]=1/5[16]=3.2`

`2^(nd)` Approximation

`x_2=1/3[11-(3.2)]=1/3[7.8]=2.6`

`y_2=1/5[16-2(3.666667)]=1/5[8.666667]=1.733333`

`3^(rd)` Approximation

`x_3=1/3[11-(1.733333)]=1/3[9.266667]=3.088889`

`y_3=1/5[16-2(2.6)]=1/5[10.8]=2.16`

`4^(th)` Approximation

`x_4=1/3[11-(2.16)]=1/3[8.84]=2.946667`

`y_4=1/5[16-2(3.088889)]=1/5[9.822222]=1.964444`

`5^(th)` Approximation

`x_5=1/3[11-(1.964444)]=1/3[9.035556]=3.011852`

`y_5=1/5[16-2(2.946667)]=1/5[10.106667]=2.021333`

`6^(th)` Approximation

`x_6=1/3[11-(2.021333)]=1/3[8.978667]=2.992889`

`y_6=1/5[16-2(3.011852)]=1/5[9.976296]=1.995259`

`7^(th)` Approximation

`x_7=1/3[11-(1.995259)]=1/3[9.004741]=3.00158`

`y_7=1/5[16-2(2.992889)]=1/5[10.014222]=2.002844`

`8^(th)` Approximation

`x_8=1/3[11-(2.002844)]=1/3[8.997156]=2.999052`

`y_8=1/5[16-2(3.00158)]=1/5[9.99684]=1.999368`

`9^(th)` Approximation

`x_9=1/3[11-(1.999368)]=1/3[9.000632]=3.000211`

`y_9=1/5[16-2(2.999052)]=1/5[10.001896]=2.000379`

`10^(th)` Approximation

`x_10=1/3[11-(2.000379)]=1/3[8.999621]=2.999874`

`y_10=1/5[16-2(3.000211)]=1/5[9.999579]=1.999916`


Solution By Gauss Jacobi Method.
`x=2.999874~=3`

`y=1.999916~=2`


This material is intended as a summary. Use your textbook for detail explanation.
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1. Example `2x+5y=21,x+2y=8`
(Previous example)
3. Example `x+y+z=3,2x-y-z=3,x-y+z=9`
(Next example)





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