Abstract: This paper is devoted to an approach of the category of projective modules of quasi-hereditary algebras of type An associated to a linearly ordered posets  with a minimal generating set consisting of exactly one generator.A characterisation of homomorphisms and the irreducible mappings is obtained.Realizing the involved algebras by the upper triangular matrices,a matrical representation of those irreducible mappings is computed.

Key words: quasi-hereditary algebra, projective module, irreducible mapping