The given system of equations is:
1) 3x - y + 2z = 18
2) 2x + 5y - 2z = 3
3) x + y - 3z = -16
Let's rearrange the equations to make them suitable for the Gauss-Jacobi method:
1) x = (18 + y - 2z) / 3
2) y = (3 - 2x + 2z) / 5
3) z = (x + y + 16) / 3
Now we can iterate through the equations using an initial guess for x, y, and z:
Initial Guess: x = 0, y = 0, z = 0
Iteration 1:
1) x = (18 + 0 - 2*0) / 3 = 18/3 = 6
2) y = (3 - 2*0 + 2*0) / 5 = 3/5
3) z = (6 + 3 + 16) / 3 = 25/3
New Approximations: x = 6, y = 0.6, z = 8.33
Continue iterating until convergence is reached or desired accuracy is obtained.
Solve the following system of equations by
Gauss-jacobi method
3x - y + 2= 18
2x + 5y - 2z = 3
x + y - 3z = -16
1 answer