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

14 GATE previous year questions on Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors (Engineering Mathematics, Civil Engineering) with answers and explanations, from every paper.

GATE 2023 CE (CE1) Q24 (1 mark, Multiple select) – If M is an arbitrary real n n matrix, then which of the following matrices will have non-negative eigenvalues?
GATE 2023 CE (CE1) Q47 (2 marks, Multiple select) – For the matrix [A] = bmatrix 1 & 2 & 3 \\ 3 & 2 & 1 \\ 3 & 1 & 2 bmatrix which of the following statements is/are TRUE?
GATE 2024 CE (CE2) Q12 (1 mark, Multiple choice) – The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication. P: (A + B)T = AT + BT Q: (AB)T =…
GATE 2024 CE (CE2) Q48 (2 marks, Numerical answer) – Consider two matrices A = bmatrix 2 & 1 & 4 \\ 1 & 0 & 3 bmatrix and B = bmatrix -1 & 0 \\ 2 & 3 \\ 1 & 4 bmatrix. The determinant of the matrix AB is…
GATE 2024 CE (CE1) Q36 (2 marks, Multiple choice) – What are the eigenvalues of the matrix bmatrix 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2 bmatrix ?
GATE 2025 CE (CE2) Q11 (1 mark, Multiple choice) – For the matrix [A] given below, the transpose is . [A] = bmatrix 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 bmatrix
GATE 2025 CE (CE2) Q45 (2 marks, Multiple select) – Pick the CORRECT eigen value(s) of the matrix [A] from the following choices. [A] = bmatrix 6 & 8 \\ 4 & 2 bmatrix
GATE 2025 CE (CE1) Q11 (1 mark, Multiple choice) – Suppose is an eigenvalue of matrix A and x is the corresponding eigenvector. Let x also be an eigenvector of the matrix B = A - 2I, where I is the…
GATE 2025 CE (CE1) Q12 (1 mark, Multiple choice) – Let A = bmatrix 1 & 1 \\ 1 & 3 \\ -2 & -3 bmatrix and b = bmatrix b 1 \\ b 2 \\ b 3 bmatrix. For Ax = b to be solvable, which one of the following…
GATE 2026 CE (CE2) Q11 (1 mark, Multiple choice) – Matrix A has the eigenvalues 1, 2, and 3. The Trace of A2 is
GATE 2026 CE (CE2) Q31 (1 mark, Numerical answer) – The eigenvalues of [A] = bmatrix 2 & -3.5 & 6 \\ 3.5 & 5 & 2 \\ 8 & 1 & 8.5 bmatrix are 1 = -1.547, 2 = 12.330, and 3 = 4.711. The absolute value of…
GATE 2026 CE (CE1) Q11 (1 mark, Multiple choice) – Matrix P is given as P = bmatrix 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 bmatrix The TRUE option is
GATE 2026 CE (CE1) Q12 (1 mark, Multiple choice) – Given: bmatrix 1 & 1 & 1 \\ 1 & 0 & 2 bmatrixBmatrix x 1 \\ x 2 \\ x 3 Bmatrix = Bmatrix 0 \\ 0 Bmatrix The above system of equations represents a
GATE 2026 CE (CE1) Q27 (1 mark, Numerical answer) – A matrix is given as bmatrix 9 & 15 \\ 15 & 50 bmatrix By performing Cholesky decomposition, l 22 of the lower triangular matrix is (*in integer*).