Q: The Gauss-Seidel iterative method for the system of equations: −(1/4)x₂ − (1/4)x₃ + x₄ = 1/4, −(1/4)x₁ + x₃ − (1/4)x₄ = 1/4, x₁ − (1/4)x₂ − (1/4)x₃ = 1/2, −(1/4)x₁ + x₂ − (1/4)x₄ = 1/2 is
(a)x₁^(n+1) = 0.5 − 0.25x₂^(n) + 0.25x₃^(n), x₂^(n+1) = 0.5 + 0.25x₁^(n+1) + 0.25x₄^(n), x₃^(n+1) = 0.25 + 0.25x₁^(n+1) + 0.25x₄^(n), x₄^(n+1) = 0.25 − 0.25x₂^(n+1) + 0.25x₃^(n+1)
(b)x₁^(n+1) = 0.5 + 0.25x₂^(n) + 0.25x₃^(n), x₂^(n+1) = 0.5 + 0.25x₁^(n+1) + 0.25x₄^(n), x₃^(n+1) = 0.25 + 0.25x₁^(n+1) + 0.25x₄^(n), x₄^(n+1) = 0.25 + 0.25x₂^(n+1) + 0.25x₃^(n+1)
(c)x₁^(n+1) = 0.5 + 0.25x₂^(n) + 0.25x₃^(n), x₂^(n+1) = 0.5 + 0.25x₁^(n+1) − 0.25x₄^(n), x₃^(n+1) = 0.25 + 0.25x₁^(n+1) − 0.25x₄^(n), x₄^(n+1) = 0.25 + 0.25x₂^(n+1) + 0.25x₃^(n+1)
(d)x₁^(n+1) = 0.5 + 0.25x₂^(n) + 0.25x₃^(n), x₂^(n+1) = 0.5 − 0.25x₁^(n+1) + 0.25x₄^(n), x₃^(n+1) = 0.25 + 0.25x₁^(n+1) + 0.25x₄^(n), x₄^(n+1) = 0.25 + 0.25x₂^(n+1) + 0.25x₃^(n+1)
Correct Answer: (b)
Detailed explanation coming soon.