Let \(a_0, a_1, \ldots, a_{r-1}\) be positive integers and define a conditional sequence \(\{q_n\}\), with initial conditions \(q_0 = 0\) and \(q_1 = 1\), and for all \(n \geq 2\), \(q_n = a_1q_{n-1} + q_{n-2}\) where \(n \equiv t \pmod{r}\). For \(r = 2\), the author studied it in \([1]\). For general \(\{q_n\}\), we found a closed form of the generating function for \(\{q_n\}\) in terms of the continuant in \([2]\). In this paper, we give the matrix representation and a Binet-like formula for the conditional sequence \(\{q_n\}\) by using the matrix methods.