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GATE 2026 MA – Question 65

Numerical Analysis · Linear Systems · 2 marks · Numerical answer

Apply Jacobi to $\begin{pmatrix}1&2&1\\0&2&2\\1&1&1\end{pmatrix}x=\begin{pmatrix}2\\2\\2\end{pmatrix}$ starting x⁽⁰⁾=(0,0,0)ᵀ. Find |x₁⁽²⁾+x₂⁽²⁾+x₃⁽²⁾| (integer).

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Correct answer: 4 to 4

Explanation

Updates are x₁(new)=2−2x₂(old)−x₃(old), x₂(new)=1−x₃(old), x₃(new)=2−x₁(old)−x₂(old). First iterate is (2,1,2); using all these old values simultaneously gives second iterate (−2,−1,−1). Absolute sum = **4**.

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