Fine spectrum of the upper triangular matrix U (r, 0, 0, s) over the sequence spaces c 0 and c Abstract Fine spectra of various matrices have been examined by several authors. In this article we have determined the fine spectrum of the upper triangular matrix U (r, 0, 0, s) on the sequence spaces c 0 and c.Let X and Y be Banach spaces and T : X → Y be a bounded linear operator. By R(T ), we denote the range of T , i.e. R(T ) = {y ∈ Y : y = T x, x ∈ X}.