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# Chapter 19. Solving Systems of Equations

When performing a scientific or engineering analysis, things aren't always as easy as solving a single equation for a single unknown. There will be many times when you will need to solve a coupled system of equations for a vector of unknowns. There are different types of systems of equations. There are underspecified systems with more unknowns than equations. There are also overspecified systems with more equations than unknowns. In this chapter we will concern ourselves with solving systems, where the number of equations and unknowns are equal. Specifically, we will create a family of methods that solve a system of equations of the form shown in Eq. (19.1).

Equation 19.1.

The system of equations shown in ...

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