Answer to Question #3280 in Algebra for Jenny

Question

Solve the system of linear equations using Jacobi's iteration method

2x+y+z=4

x+2y+z=4

x+y+2z=4

Answer 1

2x + y + z& = 4 & x = -y/2& - z/2& + 2
x + 2y + z = 4 y = -x/2& - z/2& + 2 & (1)
x + y + 2z = 4 z = -x/2& - y/2& + 2
Let’s put in right sides (1/2,& 1/2,& 1/2). So we get in first iteration
x = 3/2
y = 3/2 (2)
z = 3/2
Then& we put& (2) into (1) and get
x = 1/2
y = 1/2 (3)
z = 1/2
So we get the same . Now we add (3) and (2) and get:
x = 1
y = 1
z = 1