The k-Fibonacci sequences have first term is 0, the second term is 1, and the next term depends on a positive integer k. The k-Fibonacci numbers can represented as a k-Fibonacci matrix denoted by Fn(k). Then, the Bernoulli’s number and the Bernoulli polynomial can also be represented as the matrix and denoted by Bn and Bn(x). In this thesis, the new matrices of multiplication of the Bern…