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