GATE Engineering Mathematics: Linear algebra and matrices – Previous Year Questions

9 GATE previous year questions on Linear algebra and matrices (Engineering Mathematics, Metallurgical Engineering) with answers and explanations, from every paper.

1. GATE 2021 MT Q11 (1 mark, Multiple choice) – The eigenvalues of bmatrix1&0&-1\\0&1&0\\-1&0&1bmatrix are .
2. GATE 2022 MT Q42 (2 marks, Multiple choice) – A 33 matrix has determinant −48 and trace 8. If one eigenvalue is 4, the other two are
3. GATE 2023 MT Q30 (1 mark, Numerical answer) – The sum of eigenvalues of bmatrix4&3&2\\0&-1&2\\0&0&-3bmatrix is (integer).
4. GATE 2023 MT Q54 (2 marks, Numerical answer) – If vmatrixx+3&3x+4&4x+5\\-2&-3&-4\\-3&-4&-5vmatrix=0, then x= (integer).
5. GATE 2024 MT Q28 (1 mark, Multiple select) – Which statements are correct for a real square matrix A? Here AT denotes transpose and A-1 inverse.
6. GATE 2024 MT Q36 (2 marks, Multiple choice) – If bmatrix1&2\\8&1bmatrixbmatrixx\bmatrix=bmatrixx\bmatrix, where x,y are not both zero, the values of are
7. GATE 2025 MT Q11 (1 mark, Multiple choice) – Which one of the following matrices has eigenvalues 1 and 6?
8. GATE 2025 MT Q41 (2 marks, Multiple choice) – Which one of the following matrices is orthogonal?
9. GATE 2026 MT Q12 (1 mark, Multiple choice) – Select the correct pair of eigenvectors for the symmetric matrix A=bmatrix1&2\\2&4bmatrix.