Tridiagonal Matrices via k-Balancing Number

In this paper, we give some relations in terms of k- Balancing number which generalize some well known results concerning the relation between the determinant and Chebyshev polynomials which is due to tridiagonal matrix B(n)(k). Also for the other tridiagonal matrix W(n)(k); we deduce the cofactor matrix of it then we nd another relations for k- Balancing number.