The linear one-dimensional (1D) monoenergetic transport equation is likely the most studied transport equation in radiative transfer and neutron transport investigations. Nearly every method imaginable has been applied to establish solutions, including Laplace and Fourier transforms, singular eigenfunctions, Weiner-Hopf, PN expansions, double PN expansions, Chebychev expansions, Lagrange polynomial interpolation, numerical discrete ordinates with finite difference, analytical discrete ordinates, finite elements, integral equations, adding and doubling, invariant imbedding, solution of Ricatti equations and response matrix methods—and probably more, of which the authors are unaware. Of those listed, the response matrix solution to the discrete ordinates form of the 1D transport equation is arguably the simplest and most straightforward. Here, we propose another analytical response matrix solution based on exponentials but to the first order equation enabled by matrix scaling.