# Solve the Following Equation by Gauss Seidal Method: 10 X 1 + X 2 + X 3 = 12 2 X 1 + 10 X 2 + X 3 − 13 2 X 1 + 2 X 2 + 10 X 3 = 14 - Applied Mathematics 1

Sum

Solve the following equation by Gauss Seidal method:

10x_1+x_2+x_3=12
2x_1+10x_2+x_3-13
2x_1+2x_2+10x_3=14

#### Solution

By Gauss Seidal method ,

Given eqn : 10x_1+x_2+x_3=12
2x_1+10x_2+x_3-13
2x_1+2x_2+10x_3=14

From given eqn : |10|>|1|+|1|
|10|>|2|+|1|
|10|>|2|+|2|
The given eqn are in correct order.

therefore x_1=1/10[12-x_2-x_3]

therefore x_2=1/10[13-2x_1-x_3]

therefore x_3=1/10[14-2x_2-2x_1]

I) For 1st iteration : take x_2=0, x_3=0

x_1=1/10[12]=1.2

x_1=1.2,  x_3=0 gives x_2=1.06

x_1=1.2,  x_2=1.06 gives x_3=0.948

II) For 2nd iteration : take x_2=1.06, x_3=0.948

x_1=1/10[12-1.06-0.948]=0.9992

x_1=0.992,  x_3=0.948 gives x_2=1.0068

x_1=0.992,  x_2=1.0068 gives x_3=1.0002

III) For 3rd iteration : x_2=1.0068, x_3=1.0002

x_1=1/10[12-1.0068-1.0002]=0.9993

x_1=0.993,  x_3=1.0002 gives x_2=1.00

x_1=0.993,  x_2=1.00 gives x_3=1.00

Result : x_1=1.00, x_2=1.00, x_3=1.00

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