Matriks Pascal dan Sifat-Sifatnya

Abstract

Pascal matrices are matrices that their elements contain binomial coefficients. Pascal matrices can be built into three different types: symmetric Pascal matrix lower triangular Pascal matrix and upper triangular Pascal matrix This study aims to determine the characteristics of the Pascal matrices. The proof of characteristics shows that multiplication of a lower triangular Pascal matrix with an upper triangular Pascal matrix always yields symmetric Pascal matrix through three methods: matrix multiplication, Gaussian elimination, and equality of functions. In this study, matrix multiplication is the most effective method of proof. The proof of also shows that each of and has the same determinant value, that is one . Another characteristics of the Pascal matrix is that transpose of a lower triangular Pascal matrix is an upper triangular Pascal matrix and vice versa