# Particular generalized eigenvalue problem with parameters

If the generalized eigenvalue problem is given by $A x = u Dx$ where $D$ is a diagonal matrix with two parameters, one, say $a$ for all the diagonal elements, except the last one, say $b$. How does the eigen-system change by varying $a$ and $b$? $$D = \begin{bmatrix} a & & & & & \\ & a & & & & \\ & & a & & & \\ & & & \ddots & & \\ & & & & a & \\ & & & & & b \end{bmatrix}$$