Question #3280

Solve the system of linear equations using Jacobi's iteration method
2x+y+z=4
x+2y+z=4
x+y+2z=4

Expert's answer

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

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

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