A matrix x is a solvent of the matrix polynomials. f(x)=A o xm +…..+Am if f(x) = 0.Where A o, x, f are square matrices. In this paper we develop the linear algebra of matrix polynomials and solvents. we define division and interpolation the properties of matrices and define and study the existence of a complete set of solvents. we study the relation between the matrix polynomial problems and Theorems and lambda matrix problem, Which is to find scalar λ such that
A o λm+A1 λm-1+ ……. +Am is singular.
In a future paper we extend Cayley Hamilton Theorem for calculating of scalar polynomials to matrix polynomials. And lambda matrix for column and row Hermite calculating of lambda matrix.