Math, asked by nayakbgh97, 1 month ago

Solve 10x+y+z=12, 2x+10y+z=13, 2x+2y+10z=14 by Gauss-Seidel iteration method

Answers

Answered by llXxDramaticKingxXll
7

Step-by-step explanation:

I hope it will be help full for you

Attachments:
Answered by bhuvna789456
8

Answer:

The values are x=1,y=1,z=1.

Step-by-step explanation:

Total equations are 3.

10x+y+z=12

2x+10y+z=13,

2x+2y+10z=14.

From the above equations

x_k_+_1=\frac{1}{10}(12-y_k-z_k)

y_k_+_1=\frac{1}{10}(13-2x_k_+_1-z_k)

z_k_+_1=\frac{1}{10}(14-2x_k_+_1-2y_k_+_1)

Initial gauss (x,y,z)=(0,0,0)

Solution steps are

1^s^t Approximation

x_1=\frac{1}{10}[12-0-0]=\frac{1}{10}[12]=1.2

y_1=\frac{1}{10}[13-2(1.2)-0]=\frac{1}{10}[10.6]=1.06

z_1=\frac{1}{10}[14-2(1.2)-2(1.06)]=\frac{1}{10}[9.48]=0.948

2^n^d Approximation

x_2=\frac{1}{10}[12-1.06-0.948]=\frac{1}{10}[9.992]=0.9992

y_2=\frac{1}{10}[13-2(0.9992)-0.948]=\frac{1}{10}[10.0536]=1.0054

z_2=\frac{1}{10}[14-2(0.9992)-2(1.0054)]=\frac{1}{10}[9.9909]=0.9991

3^r^d Approximation

x_3=\frac{1}{10}[12-1.0054-0.9991]=\frac{1}{10}[9.9956]=0.9996

y_3=\frac{1}{10}[13-2(0.9996)-0.9991]=\frac{1}{10}[10.0018]=1.0002

z_3=\frac{1}{10}[14-2(0.9996)-2(1.0002)]=\frac{1}{10}[10.0005]=1.0001

4^t^h Approximation

x_4=\frac{1}{10}[12-(1.0002)-1.0001]=\frac{1}{10}[9.9998]=1

y_4=\frac{1}{10}[13-2(1)-1.0001]=\frac{1}{10}[10]=1

z_4=\frac{1}{10}[14-2(1)-2(1)]=\frac{1}{10}[10]=1

Solution By Gauss Seidel method.

x=1,y=1,z=1.

Similar questions