Some basic properties and a two-by-two matrix involving the k-Pell numbers

In this paper we consider the k-Pell numbers sequence and present some properties involving the k-Pell numbers. The theoretical basis of using generating matrices for deriving the explicit formula for the term of order n of the k-Pell numbers sequence and also to get the well-known Cassini’s identity using linear algebra. Mathematics Subject Classification: 11B37, 05A15, 11B83.