  A simple lattice model inducing a gauge theory is considered. The model
describes an interaction of a gauge field to an $N\times N$ complex matrix
scalar field transforming as a field in the fundamental representation. In
contrast to the Kazakov-Migdal model the model contains only the linear
interaction between scalar and gauge lattice fields. This model does not suffer
from extra local U(1) symmetries. In an approximation of a translation
invariant master field the large N limit of the model is investigated. At large
N the gauge fields can be integrated out yielding an effective theory
describing an interaction of eigenvalues of the master field. The reduced model
exhibits phase transitions at the points $\beta_{\bar {cr}}$ and $\beta
_{\underline{cr}}$ and the region $(\beta_{\bar{cr}}, \beta_{\underline{cr}})$
separates the strong and weak regions of the model. To study the behaviour of
the model at large $N$ in more systematic way the quenched momentum
prescription with constraints for treating the large N limit of gauge theories
is used. With the help of the technique of orthogonal polynomials nonlinear
equations describing the large N limit of the reduced model {\it with
quenching} are presented.
