We have worked extensively in the last chapter with matrices, and some with vectors. In this chapter we will develop the properties of vectors, while preparing to study vector spaces (Chapter VS). Initially we will depart from our study of systems of linear equations, but in Section LC we will forge a connection between linear combinations and systems of linear equations in Theorem SLSLC. This connection will allow us to understand systems of linear equations at a higher level, while consequently discussing them less frequently.