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GATE Engineering Mathematics: Linear Algebra: Vector algebra, matrix algebra, systems of linear equations, rank, eigenvalues and eigenvectors – Previous Year Questions

16 GATE previous year questions on Linear Algebra: Vector algebra, matrix algebra, systems of linear equations, rank, eigenvalues and eigenvectors (Engineering Mathematics, Aerospace Engineering) with answers and explanations, from every paper.

  1. GATE 2021 AE Q47 (2 marks, Numerical answer) – The ratio of the product of eigenvalues to their sum for A=bmatrix3&1&2\\2&-3&-1\\1&2&1bmatrix is (nearest integer)
  2. GATE 2022 AE Q12 (1 mark, Multiple choice) – Rotating i+ j about positive k by 135° gives
  3. GATE 2022 AE Q24 (1 mark, Multiple select) – For mutually perpendicular unit vectors a, b, c, the scalar triple product a( b c) can be
  4. GATE 2022 AE Q49 (2 marks, Numerical answer) – The largest eigenvalue of pmatrix0&1&1\\1&0&1\\1&1&0pmatrix is .
  5. GATE 2023 AE Q29 (1 mark, Multiple select) – Which statements about eigenvalues and eigenvectors are true?
  6. GATE 2023 AE Q31 (1 mark, Numerical answer) – The system x-2y+ z=0, 2x+y-4z=0, x-y+z=0 has a nontrivial solution for = (integer).
  7. GATE 2023 AE Q43 (2 marks, Multiple select) – Given A=9 i-5 j+2 k, B=11 i+4 j+ k, C=-7 i+14 j-3 k, which statements are true?
  8. GATE 2026 AE Q22 (1 mark, Multiple select) – An n n square matrix A satisfies AT = A-1. The determinant of this matrix may take which of the following value(s)?
  9. GATE 2026 AE Q32 (1 mark, Numerical answer) – If a matrix can be written as A = uvT, where both u and v are n-dimensional real-valued non-zero column vectors, then the rank of the matrix A is…
  10. GATE 2026 AE Q37 (2 marks, Multiple choice) – For the matrix A = bmatrix a & b \\ c & d bmatrix, if the relation a + b = c + d holds and a, b, c, d 0, then which one of the following statements…
  11. GATE 2025 AE Q11 (1 mark, Multiple choice) – For any real symmetric matrix A, the transpose of A is .
  12. GATE 2025 AE Q12 (1 mark, Multiple choice) – 2x + 3y + z = 0 x + y = 0 y + z = 0 The given system of equations has
  13. GATE 2025 AE Q13 (1 mark, Multiple choice) – The eigenvalues of the matrix bmatrix 1 & 2 \\ 0 & 3 bmatrix are .
  14. GATE 2024 AE Q11 (1 mark, Multiple choice) – The following system of linear equations 7x - 3y + z = 0 3x - y + z = 0 x - y - z = 0 has:
  15. GATE 2024 AE Q30 (1 mark, Numerical answer) – A particle acted upon by a constant force 4 i + j - 3 k N is displaced from point A with position vector i + 2 j + 3 k m to point B with position…
  16. GATE 2024 AE Q51 (2 marks, Numerical answer) – Consider the matrix A = bmatrix 5 & k \\ -4 & -1 bmatrix, where k is a constant. If the determinant of A is 3, then the ratio of the largest…