  We prove two inequalities regarding the ratio $\det(A+D)/\det A$ of the
determinant of a positive-definite matrix $A$ and the determinant of its
perturbation $A+D$. In the first problem, we study the perturbations that
happen when positive matrices are added to diagonal blocks of the original
matrix. In the second problem, the perturbations are added to the inverses of
the matrices.
