CHAPTER 7APPLICATIONS OF LINEAR ALGEBRA

Linear algebra has many important applications to real‐life problems. In this chapter, we concentrate on some of its applications to science and engineering. We consider applications to chemistry and chemical engineering, linear programming, Leontief input‐output model, geometry, elimination theory, coding theory and cryptography, and finally graph theory. Besides these, linear algebra also has interesting applications to image processing and computer graphics, networks, genetics, coupled linear oscillations, Markov chains, etc.

7.1 CHEMISTRY AND CHEMICAL ENGINEERING

In chemistry, we are often interested in finding a set of independent reactions among a given set of reactions.

7.1.1 Independent Reactions and Stoichiometric Matrix

In determining the composition of an equilibrium system that involves several reactions, it is important to find the minimum number of reactions that produces the same result. Consider the following set of reactions:

(7.2)equation
(7.3)equation
(7.4)equation

It is clear that the third reaction can be obtained by adding the ...

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