Question

Apply Gauss-Seidel method to solve the equation: 27 x + 6y -z = 85; 6x +15 y 2z = 72; x+y +54z =110.

Answer 1

Answer:

Solve the system of equation 27x+6y-z=85,

6x+15y+2z=72, x+y+54z=110 by Gauss

Seidel Method upto two iteration and find the

value of z.

Select one:

a. 1.92

b. 1.88

c. 0

d. 1.22

Explanation:

x=(85−6y+z)/27

y=(72−6x−2z)/15

y=(110−x−y)/54

In 1st iteration we will obtain:

y=0, z=0

x=85/27=3.14

x=3.14, z=0

y=72−(6×3.14)−2×(0)/15=3.54

x=3.14, y=3.54

z=(110−3.14−3.54)/54=1.91

In 2nd iteration we will obtain:

z=1.91, y=3.54

x=85−(6×3.54)+(1.91)/27=2.43

z=1.91, x=2.43

y=72−(6×2.43)−2×(1.91)/15=3.57

y=3.57, x=2.43

z=(110−2.43−3.57)/54=1.92

∴, after the second iteration

x=2.43

y=3.57

z=1.92.

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