Question

Solve the following system of equation by Gauss Siedal Method,20x+y-2z=17
             3x+20y-z =-18
             2x-3y+20z=𝟐𝟓

Answer 1

By Gauss Seidal method , 

Given eqn : 20x+y-2z=17
                   3x+20y-z =-18
                  2x-3y+20z=𝟐𝟓

From given eqn : |20|>|1|+|-2|

                            |20|>|3|+|-1|
                            |20|>|2|+|-3|

The given eqn are in correct order. 

∴` x=1/20[17-y+2z]`

∴ `y=1/20 [-18-3x+z]`

∴` z=1/20[25-2x+3y]`

For 1st iteration : take 𝒚=𝟎,𝒛=𝟎 

`x=1/20 [17]=0.85` 

`x=0.85,z=0        " gives"  y= -1.0275` 

`x=0.85,y=-1.0275  "gives"  x^3=1.0109`

ii) for `2^(nd)` iteration : take y=-1.0275,Z=1.0109

`x=1/20 [17+1.0275-2(1.0109)]=1.0025`

`x=1.0025, z=1.0109  "gives" y=-0.9998` 

`x=1.0025, y =-0.9998,z=0.9998` 

For `3^(rd)` iteration: y=-0.9998,z=0.9998

`x_1=1/20[17+0.9998+2(0.9998)]=1.00`

`x=1.00, z=0.9998  "gives"  y=-1.00` 

`x=1.00,y =-1.00  "gives"  z=1.00` 

Result :` x=1.00, y=-1.00z=1.00`