GATE Engineering Mathematics: Linear Algebra: Matrices and determinants, systems of linear equations, eigenvalues and eigenvectors – Previous Year Questions
11 GATE previous year questions on Linear Algebra: Matrices and determinants, systems of linear equations, eigenvalues and eigenvectors (Engineering Mathematics, Biotechnology) with answers and explanations, from every paper.
- GATE 2021 BT Q54 – The determinant of A=pmatrix1&1&1&1\\-1&1&1&1\\-1&-1&1&1\\1&1&1&3pmatrix is .
- GATE 2022 BT Q12 – If eigenvalues of a 22 matrix P are 4 and 2, the eigenvalues of P-1 are
- GATE 2022 BT Q39 – A 22 matrix P has eigenvalue 2 with eigenvector (1,0)T and eigenvalue 5 with eigenvector (1,1)T. What is P?
- GATE 2023 BT Q58 – If A=pmatrix1&2\\3&5pmatrix, the value of A4+3A2-5A+6I is .
- GATE 2026 BT Q12 – Which of the following is one of the eigenvalues for the matrix given below? bmatrix 3 & 4 \\ 4 & -3 bmatrix
- GATE 2026 BT Q41 – For the given matrix, which of the statements given below is/are true? bmatrix 3 & 1 & 5 \\ 2 & -1 & 0 \\ 5 & 2 & 9 bmatrix
- GATE 2025 BT Q34 – The value of k, for which the linear equations 2x + 3y = 6 and 4x + 6y = 3k have at least one solution, is . (Answer in integer)
- GATE 2025 BT Q63 – Let A = pmatrix1 & 0 & 1\\0 & k & 0\\3 & 0 & -1pmatrix. If the eigenvalues of A are -2, 1, and 2, then the value of k is . (Answer in integer)
- GATE 2024 BT Q28 – A value of k for which the linear equations (k-1)x + 3y = 0 and 2x + ky = 0 have a non-zero solution is .
- GATE 2024 BT Q32 – Let OR be the vector that is perpendicular to the vectors OP = 2 i - 3 j + k and OQ = -2 i + j + k. If the length of the vector OR is 3, then is .
- GATE 2024 BT Q62 – If v = pmatrix2\\2\\2pmatrix is an eigenvector of the matrix pmatrix1&2&3\\1&2&3\\1&2&3pmatrix corresponding to the non-zero eigenvalue, , then the…