  We will explore some properties of minimal graded free resolutions of $R/I$,
where $R$ is a trivariate polynomial ring over a field and $I$ is a monomial
ideal. Our focus will be to consider a specific form of the resolutions when
$I$ is primary to the homogeneous maximal ideal. We will identify certain
characteristics of the last matrix of these resolutions, and observe
differences in the resolutions for generic ideals in comparison to non-generic
ideals. Finally, we learn how to identify whether $I$ is generic by knowing the
structure of the last matrix in the minimal free resolution of $R/I$.
