GATE 2016 ME (ME1) – Question 39
Use Gauss–Seidel in the given equation order: $x_1+2x_2+3x_3=5$, $2x_1+3x_2+x_3=1$, $3x_1+2x_2+x_3=3$. With $x_1=x_2=x_3=0$ initially, $x_3$ after the first iteration is ______.
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Correct answer: -6 to -6
Explanation
Starting from all zeros, the first equation gives x1=5. Use that updated value in the second: x2=(1−2·5−0)/3=−3. Use both updated values in the third: x3=3−3·5−2(−3)=**−6**. Using old values throughout would instead be Jacobi iteration.