ABSTRACT
In this chapter we introduce the reader to the notion of vector space by pre- senting two classical examples: Tuples and Matrices. These are concrete examples which will prepare the student for the general definition in Chapter 3. We also begin the process of providing the student with the computational skills necessary for the subject of Linear Algebra. In Section 1.1, the first example of a vector space, Tuples, is introduced. In Section 1.2, the operation dot product for Tuples is presented as a precursor for Chapter 5 which discusses general inner product spaces. Section 1.3 is our first application section and shows how one can use vectors in R2 or R3 in order to prove in a new way facts about Euclidean geometry. In Section 1.4, the second example of a vector space, Matrices, is introduced. Finally, in Section 1.5, we define multiplication of matrices.
