  We discuss the Penner-type matrix model which has been proposed to explain
the AGT relation between the 2-dimensional Liouville theory and 4-dimensional
N=2 superconformal gauge theories. In our previous communication we have
obtained the spectral curve of the matrix model and showed that it agrees with
that derived from M-theory. We have also discussed the decoupling limit of
massive flavors and proposed new matrix models which describe Seiberg-Witten
theory with flavors N_f=2,3. In this article we explicitly evaluate the free
energy of these matrix models and show that they in fact reproduce the
amplitudes of Seiberg-Witten theory.
