Let $S = \{\lambda_1, \cdots, \lambda_n\}$ be an ordered set of $n$ real numbers, not all equal, but not all necessarily distinct. Pick out the true statements:
a. There exists an $n\times n$ matrix with complex entries, which is not self-adjoint, whose set of eigenvalues is given by $S$.
b. There exists an $n\times n$ self-adjoint, non-diagonal matrix with complex entries whose set of eigenvalues is given by $S$.
c. There exists an $n\times n$ symmetric, non-diagonal matrix with real entries whose set of eigenvalues is given by $S$.
a) No Idea.
b) as hermitian matrices(self adjoint) matrices has real eigen values only so $b$ may be true..
c) same logic as $b$. please help.