GATE Engineering Mathematics: Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors – Previous Year Questions

6 GATE previous year questions on Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors (Engineering Mathematics, Mechanical Engineering) with answers and explanations, from every paper.

1. GATE 2022 ME (ME1) Q15 (1 mark, Multiple choice) – If A = bmatrix 10 & 2k + 5 \\ 3k - 3 & k + 5 bmatrix is a symmetric matrix, the value of k is .
2. GATE 2022 ME (ME1) Q46 (2 marks, Multiple select) – The system of linear equations in real (x, y) given by (x\ \ y)bmatrix 2 & 5 - 2 \\ & 1 bmatrix = (0\ \ 0) involves a real parameter and has…
3. GATE 2023 ME Q32 (1 mark, Numerical answer) – A linear transformation maps a point (x, y) in the plane to the point (x, y) according to the rule x = 3y, y = 2x. Then, the disc x2 + y2 1 gets…
4. GATE 2024 ME Q14 (1 mark, Multiple choice) – Consider the system of linear equations x + 2y + z = 5 2x + ay + 4z = 12 2x + 4y + 6z = b The values of a and b such that there exists a non-trivial…
5. GATE 2024 ME Q36 (2 marks, Multiple choice) – The matrix bmatrix 1 & a \\ 8 & 3 bmatrix (where a > 0) has a negative eigenvalue if a is greater than
6. GATE 2025 ME Q11 (1 mark, Multiple choice) – Let **A** and **B** be real symmetric matrices of same size. Which one of the following options is correct?