List of top Mathematics Questions on Linear Algebra asked in AP PGECET

Let \( A = \begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} \) be a 3 × 3 matrix. If \( \alpha \) and \( \beta \) are the largest and smallest eigenvalues of \( A \), respectively, then \( \alpha - \beta = \_\_\_\_\_\_ \)
If the determinant of the 3 × 3 matrix \( A = \begin{pmatrix} a & 1 & 2 \\ b & 0 & -2 \\ 1 & -3 & 1 \end{pmatrix} \) is zero, then the values of \( a \) and \( b \) are: