The GATE Grind

GATE Mathematics Foundation: Linear Algebra – Previous Year Questions

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

  1. GATE 2021 ES Q36 (2 marks, Multiple choice) – P+Q=pmatrix3&1\\2&12pmatrix and P-Q=pmatrix-1&-7\\8&2pmatrix. Find Q.
  2. GATE 2022 ES Q14 (1 mark, Multiple choice) – P is m×n, Q is n×l, R and S are n×n. Assess I:(PQ)T=QTPT; II:(RS)-1=S-1R-1.
  3. GATE 2022 ES Q37 (2 marks, Multiple choice) – Find eigenvalues of pmatrix0&1\\-2&3pmatrix.
  4. GATE 2023 ES Q12 (1 mark, Multiple choice) – For square matrices P, Q, consider X:(P-1)-1=P and Y:Q is symmetric if Q=-QT. Choose the truth values.
  5. GATE 2023 ES Q48 (2 marks, Numerical answer) – P=pmatrix2&3\\1&4pmatrix,Q=pmatrix5&4\\0&2pmatrix and R=(PQ)T. Find det R as an integer.
  6. GATE 2024 ES Q24 (1 mark, Multiple select) – Select the eigenvalues of pmatrix4&3\\3&4pmatrix.
  7. GATE 2024 ES Q25 (1 mark, Multiple select) – For a vector X, linear operators A, B and scalar λ,which identities hold?
  8. GATE 2025 ES Q48 (2 marks, Numerical answer) – Solve x-2y+z=34, 2x+y+z=102, x+y-3z=17. Find x+y+z,to two decimals.
  9. GATE 2026 ES Q11 (1 mark, Multiple choice) – Find the matrix X satisfying 2X+pmatrix1&2\\3&4pmatrix=pmatrix3&8\\7&2pmatrix.
  10. GATE 2026 ES Q37 (2 marks, Multiple choice) – Find the eigenvalues of A=pmatrix2&2&3\\2&5&6\\3&4&10pmatrix.
  11. GATE 2026 ES Q42 (2 marks, Multiple select) – For AX=B,where A=pmatrix2&5\\5&-2pmatrix and B=pmatrix7\\3pmatrix,which statements are true? Select all that apply.