Let

where B and C are square matrices.
(a) If λ is an eigenvalue of B with eigenvector x = (x1,..., xk)T, show that λ is also an eigenvalue of A with eigenvector = (x1,..., xk, 0,..., 0)T.
(b) If B and C are positive matrices, show that A has a positive real eigenvalue r with the property that |λ| (c) If B = C, show that the eigenvalue r in part (b) has multiplicity 2 and possesses a positive eigenvector.

A-H 0