The GATE Grind

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

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

  1. GATE 2021 IN Q11 (1 mark, Multiple choice) – Consider row vectors v=(1,0) and w=(2,0). The rank of M=2vTv+3wTw, where T denotes transpose, is .
  2. GATE 2021 IN Q35 (1 mark, Numerical answer) – The determinant of M=bmatrix1&2&0&0\\3&4&0&0\\0&0&4&3\\0&0&2&1bmatrix is .
  3. GATE 2021 IN Q48 (2 marks, Numerical answer) – For A=bmatrix2&5\\0&3bmatrix, the determinant (A4-5A3+6A2+2I) is .
  4. GATE 2022 IN Q24 (1 mark, Multiple select) – Given M=bmatrix2&3&7\\6&4&7\\4&6&14bmatrix, which statements are correct?
  5. GATE 2022 IN Q49 (2 marks, Multiple select) – Matrix A=bmatrix4&3\\9&-2bmatrix has eigenvalues −5 and 7. Select its eigenvector(s).
  6. GATE 2023 IN Q11 (1 mark, Multiple choice) – Choose the solution set S of x-2y+z=0 and x-z=0. Here R denotes the real numbers; tuples denote column vectors.
  7. GATE 2023 IN Q63 (2 marks, Numerical answer) – The matrix A=bmatrix1&4\\-3&\\&6bmatrix has rank one. The ratio / is (nearest integer).
  8. GATE 2024 IN Q19 (1 mark, Multiple choice) – A matrix M=[v 1\ v 2\ v 3] is formed by stacking three column vectors. Which set gives rank(M)=3? Tuples below denote column vectors.
  9. GATE 2024 IN Q26 (1 mark, Numerical answer) – A real 33 matrix P has eigenvalues 1/4,1,-2. The determinant P-1 is (nearest integer).
  10. GATE 2025 IN Q11 (1 mark, Multiple choice) – A 2n2n matrix A=[a ij] has elements a ij=cases,&i+j odd,\\-,&i+j even.cases Here n is any integer greater than 2 and is any nonzero real number. The…
  11. GATE 2025 IN Q32 (1 mark, Numerical answer) – One eigenvector of A=bmatrix-1&-1\&-4bmatrix is along bmatrix\\2bmatrix, where is any nonzero real number. The value of x is (in integer).
  12. GATE 2026 IN Q11 (1 mark, Multiple choice) – A matrix PR33 satisfies P3-4P2+5P-2I=0, where I is a 33 identity matrix. The set of all possible eigenvalues of matrix P is .
  13. GATE 2026 IN Q14 (1 mark, Multiple choice) – Consider the matrix A=bmatrix1&0&2\\-1&1&0\\0&1&2bmatrix. Let b=bmatrix1\\3\\0bmatrix, x=bmatrixx 1\ 2\ 3bmatrix. The number of solutions to the…