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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