The Jones polynomial is an important knot invariant introduced in 1984 by Vaughn Jones. There are multiple ways to compute the Jones polynomial and in this paper we will explore a technique introduced by L. Zulli using trip matrices. In particular, we will focus on using trip matrices to compute the Jones polynomial of T(2,n) torus knots. Jones proved an explicit formula for the Jones Polynomial of all torus knots, but the proof relies on heavy machinery from Abstract Algebra. We provide a more elementary proof of this formula for T(2, n) knots using trip matrices and basic Linear Algebra.