GATE Numerical Analysis: Linear Systems – Previous Year Questions

5 GATE previous year questions on Linear Systems (Numerical Analysis, Mathematics) with answers and explanations, from every paper.

1. GATE 2022 MA Q25 (1 mark, Multiple select) – For Ax=b, A=pmatrix3&1&1\\1&4&1\\2&0&3pmatrix and b=(2,3,4)ᵀ, select all true statements.
2. GATE 2023 MA Q40 (2 marks, Multiple choice) – For Mx=b, M=pmatrix2&-1\\-4&3pmatrix and b=(−2,5)ᵀ. P:if M=LU with lower triangular L having unit diagonal, trace U=3. Q:Jacobi iterates converge to…
3. GATE 2024 MA Q21 (1 mark, Multiple choice) – A=pmatrix2&-1&1\\1&2&-1\\-1&1&2pmatrix. For (A+εI)x=b, ε>0, I: Jacobi converges for every start. II: Gauss–Seidel converges for every start. Choose…
4. GATE 2025 MA Q36 (2 marks, Multiple choice) – For Ax=b with nonzero diagonal D, D-1A=pmatrix1&1&-2\\3&1&2\\1&1&1pmatrix and D⁻¹b=(4,4,1)ᵀ. S1: Jacobi from x⁽⁰⁾=(1,1,1)ᵀ gives x⁽¹⁾=(5,−1,−1)ᵀ. S2:…
5. GATE 2026 MA Q65 (2 marks, Numerical answer) – Apply Jacobi to pmatrix1&2&1\\0&2&2\\1&1&1pmatrixx=pmatrix2\\2\\2pmatrix starting x⁽⁰⁾=(0,0,0)ᵀ. Find x₁⁽²⁾+x₂⁽²⁾+x₃⁽²⁾ (integer).