List of top Mathematics Questions on Linear Algebra asked in IIT JAM PH

If the system of linear equations
x + my + az = 0
2x + ay + mz = 0
ax + 2y - z = 0
with m and a as non-zero constants, admits a non-trivial solution, then which one of the following conditions is correct?

If \(P\) and \(Q\) are Hermitian matrices, which of the following is/are true?
(A matrix \(P\) is Hermitian if \(P = P^{\dagger}\), where the elements \(p_{ij}^{\dagger} = p_{ji}^{*}\))

The eigenvalues of

\[ \begin{pmatrix} 3 & i & 0 \\ -i & 3 & 0 \\ 0 & 0 & 6 \end{pmatrix} \]

are