Linear algebra is increasingly important in applications to many areas. To illustrate this statement, two problems in mathematical biology are considered. The first concerns target reproduction numbers as threshold parameters. These are defined, their properties investigated, and then applied to the projection matrix of an invasive weed having three life stages, with the aim of controlling the weed. The second concerns the spread of an infectious disease, such as cholera, in a heterogeneous environment modeled as a community network. The impact of varying the network on the basic reproduction number is quantified by using a group inverse, and control strategy investigated.