GATE Engineering Mathematics: Linear Algebra – Previous Year Questions

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

1. GATE 2021 AG Q22 (1 mark, Numerical answer) – Find the trace of pmatrix3&2&1&4\\5&7&8&1\\2&4&6&7\\9&6&4&2pmatrix as an integer.
2. GATE 2021 AG Q50 (2 marks, Numerical answer) – Find sum of eigenvalues of pmatrix4&1\\3&6pmatrix,rounded to an integer.
3. GATE 2022 AG Q11 (1 mark, Multiple choice) – The determinant of a matrix remains unaltered if .
4. GATE 2022 AG Q37 (2 marks, Multiple choice) – For what listed values of x is pmatrix3-x&2&2\\2&4-x&1\\-2&-4&-1-xpmatrix singular?
5. GATE 2023 AG Q11 (1 mark, Multiple choice) – A, B are3×3 matrices with A =-1, B =3. Find 3AB .
6. GATE 2023 AG Q36 (2 marks, Multiple choice) – A=pmatrix1&-1\\2&-1pmatrix,B=pmatrixa&1\&-1pmatrix and (A+B)2=A2+B2. Find a, b.
7. GATE 2024 AG Q36 (2 marks, Multiple choice) – Given P=pmatrix2&3&7\\4&1&5pmatrix and Q=pmatrix8&11&9\\12&6&13pmatrix,find PTQ.
8. GATE 2025 AG Q11 (1 mark, Multiple choice) – If a, b, c are the roots of 2x3-3x2+px-1=0 and two roots sum to 1,find p.
9. GATE 2025 AG Q12 (1 mark, Multiple choice) – If pmatrixx&-3\\2&x-5pmatrix is singular, find the sum of possible x values.
10. GATE 2026 AG Q14 (1 mark, Multiple choice) – Square matrices A,B of the same order satisfy (AB)=-80 and A=5. Find (BT).
11. GATE 2026 AG Q37 (2 marks, Multiple choice) – A 2×2 matrix has determinant 1.6 and eigenvalue sum −2.8. Find its eigenvalues.