Question

10x+y+z=12,X+10y+z=12,X+y+10z=12 solve the equation by using Gauss Seidel method

Answer 1

Answer: 10x+y+z=12⋯(1)

2x+10y+z=13⋯(2)

2x+2y+10z=14⋯(3)

(1)−(2)

8x−9y=−1

8x=9y−1

x=  

8

9y−1

​

⋯(4)

(2)−(3)

8y−9z=−1

9z=1+8y

z=  

9

1+8y

​

⋯(5)

⟹10(  

8

9y−1

​

)+y+(  

9

1+8y

​

)=12

405y−45+36y+4+32y=432

473y=473

y=1

⟹x=  

8

9(1)−1

​

=1

⟹z=  

9

1+8(1)

​

=1