The GATE Grind

GATE Engineering Mathematics: Linear Algebra: Eigen values, Eigen vectors – Previous Year Questions

12 GATE previous year questions on Linear Algebra: Eigen values, Eigen vectors (Engineering Mathematics, Electrical Engineering) with answers and explanations, from every paper.

  1. GATE 2017 EE Q11 (1 mark, Multiple choice) – The matrix A = bmatrix 32 & 0 & 12 \\ 0 & -1 & 0 \\ 12 & 0 & 32 bmatrix has three distinct eigenvalues and one of its eigenvectors is bmatrix 1 \\ 0…
  2. GATE 2015 EE Q36 (2 marks, Multiple choice) – The maximum value of "a" such that the matrix pmatrix -3 & 0 & -2 \\ 1 & -1 & 0 \\ 0 & a & -2 pmatrix has three linearly independent real eigenvectors…
  3. GATE 2016 EE Q12 (1 mark, Numerical answer) – Consider a 3 3 matrix with every element being equal to 1. Its only non-zero eigenvalue is .
  4. GATE 2016 EE Q38 (2 marks, Multiple choice) – Let the eigenvalues of a 2 2 matrix A be 1, -2 with eigenvectors x 1 and x 2 respectively. Then the eigenvalues and eigenvectors of the matrix A2 - 3A…
  5. GATE 2018 EE Q54 (2 marks, Numerical answer) – Let A=bmatrix1&0&-1\\-1&2&0\\0&0&-2bmatrix and B=A3-A2-4A+5I, where I is the 33 identity matrix. The determinant of B is (up to 1 decimal place).
  6. GATE 2019 EE Q12 (1 mark, Multiple choice) – M is a 22 matrix with eigenvalues 4 and 9. The eigenvalues of M2 are
  7. GATE 2021 EE Q11 (1 mark, Multiple choice) – Let p and q be real numbers such that p2+q2=1. The eigenvalues of the matrix bmatrixp&q\&-pbmatrix are
  8. GATE 2021 EE Q48 (2 marks, Numerical answer) – Let A be a 1010 matrix such that A5 is a null matrix, and let I be the 1010 identity matrix. The determinant of A+I is .
  9. GATE 2022 EE Q40 (2 marks, Multiple choice) – eA denotes the exponential of a square matrix A. Suppose is an eigenvalue and v is the corresponding eigen-vector of matrix A. Consider the following…
  10. GATE 2024 EE Q32 (1 mark, Numerical answer) – The sum of the eigenvalues of the matrix A=bmatrix1&2\\3&4bmatrix2 is (rounded off to the nearest integer).
  11. GATE 2025 EE Q12 (1 mark, Multiple choice) – Let v 1 and v 2 be the two eigenvectors corresponding to distinct eigenvalues of a 33 real symmetric matrix. Which one of the following statements is…
  12. GATE 2026 EE Q30 (1 mark, Multiple select) – Two n n matrices A and B have a common eigenvalue 2, and the same corresponding nonzero eigenvector. Which of the following options is/are correct?…