List of top Mechanical Engineering Questions on Linear Algebra asked in AP PGECET

The system of equation \(x - y + 3z = 0, x + z = 0, x + y - z = 0\) has _______

Let \(A = \begin{pmatrix} 2026 & 2025 & 2024 \\ 2025 & 2024 & 2023 \\ 2024 & 2023 & 2023 \end{pmatrix}\) be a matrix. Then, \(\det(A)\) is equal to _______

If a \(2 \times 2\) matrix \(A\) has eigenvalues 1 and 4 with the corresponding eigenvectors \(\begin{pmatrix} 1 \\ -1 \end{pmatrix}\) and \(\begin{pmatrix} 2 \\ 1 \end{pmatrix}\), respectively, then \(A\) is ________

Let \(A = \begin{pmatrix} 2026 & 2025 & 2024 \\ 2025 & 2024 & 2023 \\ 2024 & 2023 & 2023 \end{pmatrix}\) be a matrix. Then, \(\det(A)\) is equal to _______

If a \(2 \times 2\) matrix \(A\) has eigenvalues 1 and 4 with the corresponding eigenvectors \(\begin{pmatrix} 1 \\ -1 \end{pmatrix}\) and \(\begin{pmatrix} 2 \\ 1 \end{pmatrix}\), respectively, then \(A\) is ________

The system of equation \(x - y + 3z = 0, x + z = 0, x + y - z = 0\) has _______