Koken, Fikri2024-02-232024-02-2320202651-477Xhttps://doi.org/10.15672/hujms.481026https://hdl.handle.net/20.500.12452/15500In this study, a matrix R-v is defined, and two closed form expressions of the matrix R-v(n), for an integer n >= 1, are evaluated by the matrix functions in matrix theory. These expressions satisfy a connection between the generalized Fibonacci and Lucas numbers with the Pascal matrices. Thus, two representations of the matrix R-v(n) and various forms of matrix (R-v +q Delta I)(n) are studied in terms of the generalized Fibonacci and Lucas numbers and binomial coefficients. By modifying results of 2 x 2 matrix representations given in the references of our study, we give various 3 x 3 matrix representations of the generalized Fibonacci and Lucas sequences. Many combinatorial identities are derived as applications.eninfo:eu-repo/semantics/openAccessGeneralized Fibonacci And Lucas SequencesGeneralized Fibonacci And Lucas MatricesPascal MatricesArticle495173517432-s2.0-85092935168WOS:000581099500016Q310.15672/hujms.481026