Quantitative Methods: An Introduction for Business Management

3

Linear Algebra

This chapter contains some very basic and some relatively advanced material, which is needed only in a few later chapters. Hence, it can be read in quite different ways, depending on readers' interest:

• Readers interested in elementary probability and statistics (Chapters 4–11) may just have a look at Sections 3.1 and 3.2, which motivate and illustrate basic approaches to solve systems of linear equations; this is an important topic that any reader should be familiar with.
• The remaining sections of this chapter are more advanced, but they are mostly needed by those interested in the multivariate statistics techniques described in Chapters 15–17. One possibility is reading this whole chapter now; alternatively, one might prefer just having a cursory look at the material, and returning here when tackling those chapters.
• Finally, readers who are interested in optimization modeling can do the same when grappling with Chapter 12. Some concepts related to quadratic forms (Section 3.8) and multivariable calculus (Section 3.9) are useful to obtain a better grasp of some technical aspects of optimization. Apparently, these are not necessary if you are just interested in building an optimization model, but not in the algorithms needed to solve it; nevertheless, an appreciation of what a convex (i.e., easy-to-solve) optimization model is better gained if you are armed with the background we build here.

In Section 3.1 we propose a simple motivating example related to pricing ...