  The $SU(3)$ Yang-Mills matrix model coupled to fundamental fermions is an
approximation of quantum chromodynamics (QCD) on a 3-sphere of radius $R$. The
spectrum of this matrix model Hamiltonian is estimated using standard
variational methods, and is analyzed in the strong coupling limit. By employing
a matching prescription to determine the dependence of the Yang-Mills coupling
constant $g$ on $R$, we relate the asymptotic values of the energy eigenvalues
in the $R \rightarrow \infty$ (flat space) limit to the masses of light
hadrons. We find that the matrix model estimates the light hadron spectrum
fairly accurately, with the light baryon masses falling within $10\%$, and most
light meson masses falling within about $30\%$ of their observed values.
