Some students will have studied elementary linear algebra already, but many will not, so the topic is treated starting from scratch. The basic properties of vectors and matrices and the usual operations of addition and multiplication are covered in the first two sections.
Section 8.3 treats linear equations, including dependence and consistency, and the usual algorithm for solution. In Section 8.4 the reduced row echelon form is described, together with more on the classification of systems of equations. Matrix inverses are calculated and applied.
The chapter concludes with a discussion of adjacency matrices and the application of matrices to graphs and relations.