GATE Engineering Mathematics: Linear Algebra – Previous Year Questions

8 GATE previous year questions on Linear Algebra (Engineering Mathematics, Mining Engineering) with answers and explanations, from every paper.

1. GATE 2021 MN Q22 (1 mark, Multiple choice) – Which statement is true for a real symmetric positive-definite square matrix?
2. GATE 2023 MN Q27 (1 mark, Multiple choice) – Matrix A is negative definite. Which statement is NOT correct? Use the conventional real symmetric matrix definition.
3. GATE 2023 MN Q41 (2 marks, Multiple choice) – Three straight-line equations have (slope, intercept) pairs (2, 3), (4, 5), and (6, 2). Classify the simultaneous system.
4. GATE 2024 MN Q38 (2 marks, Multiple choice) – Given A=pmatrix1&4&3\\5&2&1\\6&4&3pmatrix, classify B=A-AT.
5. GATE 2025 MN Q14 (1 mark, Multiple choice) – A3×3 matrix has rank2. Find its determinant.
6. GATE 2025 MN Q55 (2 marks, Numerical answer) – The characteristic polynomial is x3-6x2+11x-6. One eigenvalue is1. Find the sum of the other two,as an integer.
7. GATE 2026 MN Q11 (1 mark, Multiple choice) – For P=pmatrix2&1\\0&3pmatrix and identity I, which polynomial identity follows from Cayley–Hamilton?
8. GATE 2026 MN Q38 (2 marks, Multiple choice) – Let x=(1,2,1)T, b=(-16,-3,7)T, and P-1=pmatrixe&-6&-7\&9&11\\-1&-2&gpmatrix. Given Px=b and Py=d with d=(-16,0,7)T, find y₂.