Figure 2.1: A system of two linear equations with two unknowns, with a unique
There is no way to draw two straight lines on a plane so that they only
intersect twice. In fact, there are only three possibilities for two lines on a
plane: they never intersect, intersect once, or intersect an infinite number of
times. Hence, a system of two equations with two unknowns can have either
no solution, a unique solution, or an infinite number of solutions.
Linear algebra is about such systems of linear equations, but with many
more equations and unknowns.
Many practical problems benefit from in-
sights offered by linear algebra. Later in this chapter, as an example of how
linear algebra arises in real problems, we explore the analysis of contingent
claims. Our primary motivation for studying linear algebra, however, is to
develop a foundation for linear programming, which is the main topic of this
book. Our coverage of linear algebra in this chapter is neither self-contained
nor comprehensive. A couple of results are stated without any form of proof.
The concepts presented are chosen based on their relevance to the rest of the