Question

Solve the following equation by Gauss-Seidel Method up to 2 iterations and find the value of z. X1 + X2 + 25x3 10 6x1 + 15x2 + 2x3 -8 10x1 + 6x2 – X3 = 6 Give answer in 3-decimal plates.(Like 1.222) = r Answer:

Answer 1

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.

10x+6y-z=6

6x+15y+2z=-8

x+y+25z=10

From the above equations

x_k+1=1(6-6y_k+z_k)/10

y_k+1=(-8-6x_k+1-2z_k)/15

z_k+1=(10-x_k+1-y_k+1)/25

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

Step. 1.

x₁=0.6, y₁=-77333, z₁=0.4069

Step. 2.

x₂=1.1046, y₂= - 1.0294, z₃=0.3969

Therefore solution is (1.105,-1.029,0.397