  We study the problem of maximum likelihood estimation for $3$-dimensional
linear spaces of $3\times 3$ symmetric matrices from the point of view of
algebraic statistics where we view these nets of conics as linear concentration
or linear covariance models of Gaussian distributions on $\mathbb{R}^3$. In
particular, we study the reciprocal surfaces of nets of conics which are
rational surfaces in $\mathbb{P}^5$. We show that the reciprocal surfaces are
projections from the Veronese surface and determine their intersection with the
polar nets. This geometry explains the maximum likelihood degrees of these
linear models. We compute the reciprocal maximum likelihood degrees. This work
is based on Wall's classification of nets of conics from 1977.
