For a long times researchers have been working on recurrence relation sequences of Fibonacci numbers and Fibonacci polynomials which are useful topic not only in mathematics but also in physics, management and various applications in many other fields. There are many useful identities on recurrence relation Fibonacci sequence but there main problem to find any term of recurrence relation Fibonacci sequence we need to find previous all terms of recurrence relation Fibonacci sequence of numbers and polynomials. There were many important theorems obtained on recurrence relation k-Fibonacci sequences. We also published a paper on generating matrix for Fibonacci sequence of number and polynomials but in this paper we extend this result for k-Fibonacci sequence of numbers so we can say that it extension of previous result generating matrix for Fibonacci recurrence relation sequence of number now this result extended up to k-Fibonacci recurrence relation sequence of number. In this paper we have given special types of matrix for generalized k-Fibonacci recurrence relation sequence of number. These matrices and their determinant are very useful to represent k-Fibonacci generalized sequence of numbers in the form of matrix. Authors define a special formula in this paper by this we can find special representation of k-Fibonacci generalized sequence of numbers in the form of matrix. So, we can say that this paper is generalization of property of k-Fibonacci sequence of number. So finally, we can say that this theorem is valid all order of k-Fibonacci sequence of numbers. So, we can say that this paper is generalization of property of a relation between coefficients of recurrence relation terms and determinant of matrix. So we can say this paper is representation of k-Fibonacci sequence of number in term of special type sequence of determinant.

Generalized, recurrence relation, sequence, matrix.