  The linear 1D transport equation is likely the most solved 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, solutions of singular integral
equation, PN expansions, double PN expansions, Chebychev expansions, Lagrange
polynomial expansions, numerical discrete ordinates with finite difference,
analytical discrete ordinates, finite elements, solutions to integral
equations, adding and doubling, invariant imbedding, solution of Ricatti
equations and response matrix methods -- and probably more methods 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 response of exponential
solutions but to the first order equation enabled by matrix scaling.
