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Question
Gauss-Seidel method is used to solve the following equations (as per the given order):
x1+2x2+3x3=5,
2x1+3x2+x3=1
3x1+2x2+x3=3
Assuming initial guess as x1=x2=x3=0, the value of x3 after the first iteration is
- -6
x1+2x2+3x3=5,
2x1+3x2+x3=1
3x1+2x2+x3=3
Assuming initial guess as x1=x2=x3=0, the value of x3 after the first iteration is
- -6
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Solution
The correct option is A -6
Given that
x1=x2=x3=0
Hence,
x1+2(0)+3(0)=5
x1=5
Now for x2, we have x1=5 & x3=0
i.e.,2x1+3x2+0=1
⇒ 3x2=1−2x1
⇒ 3x2=1−2(5)=−9
∵ x2=−3
Now for x3, we will take x1=5 & x2=−3
i.e.,3x1+2x2+x3=3
x3=3−3x1−2x2
x3=3−3(5)−2(−3)=−6
Hence, -6 is correct.
Note: Here we have not changed given system into diagonally dominant system as it is mentioned that we have to solve this system "As per the given order".
Given that
x1=x2=x3=0
Hence,
x1+2(0)+3(0)=5
x1=5
Now for x2, we have x1=5 & x3=0
i.e.,2x1+3x2+0=1
⇒ 3x2=1−2x1
⇒ 3x2=1−2(5)=−9
∵ x2=−3
Now for x3, we will take x1=5 & x2=−3
i.e.,3x1+2x2+x3=3
x3=3−3x1−2x2
x3=3−3(5)−2(−3)=−6
Hence, -6 is correct.
Note: Here we have not changed given system into diagonally dominant system as it is mentioned that we have to solve this system "As per the given order".
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