To solve this system of equations using Gauss-Jacobi method, we need to rewrite each equation in the form of x, y, and z on the left side:
1) x - 2y + z = 30.6
2) 2x + 5y + z = 10.5
3) 3x + y + z = 9.3
Now, let's rewrite the equations in matrix form as follows:
[1 -2 1] [x] [30.6]
[2 5 1] [y] = [10.5]
[3 1 1] [z] [9.3]
Next, let's initialize the initial guess for x, y, and z. Let's say x₀ = 0, y₀ = 0, z₀ = 0.
Now, we'll use the following iterations to find the approximate values of x, y, and z:
1) x₁ = (30.6 + 2*0 + 0)/1 = 30.6
2) y₁ = (10.5 - 2*0 - 0)/5 = 2.1
3) z₁ = (9.3 - 3*0 - 2.1)/1 = 7.2
Now, our new approximate solution is x₁ = 30.6, y₁ = 2.1, z₁ = 7.2
Repeat the process until the values of x, y, and z converge to a solution.
Solve the following system of equations by
Gauss-jacobi method
x - 2y + 10 = 30.6
2x + 5y - z = 10.5
3x + y + z = 9.3
1 answer