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Erschienen in:
2018 | OriginalPaper | Buchkapitel
1. LINEAR SYSTEMS OF EQUATIONS
verfasst von : Thomas S. Shores
Erschienen in: Applied Linear Algebra and Matrix Analysis
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Abstract
Welcome to the world of linear algebra. The two central problems about which much of the theory of linear algebra revolves are the problem of finding all solutions to a linear system and that of finding an eigensystem for a square matrix. The latter problem will not be encountered until Chapter 5; it requires some background development and the motivation for this problem is fairly sophisticated. By contrast, the former problem is easy to understand and motivate. As a matter of fact, simple cases of this problem are a part of most high-school algebra backgrounds. We will address the problem of existence of solutions for a linear system and how to solve such a system for all of its solutions. Examples of linear systems appear in nearly every scientific discipline; we touch on a few in this chapter.