Game Development Reference
In-Depth Information
chapter 11
Systems and Matrices
In this chapter, you explore how to find the solutions to equations that possess
two variables. One of the most ready ways of solving such equations involves
substitution. Given this groundwork, you then explore how to work with systems
of equations that involve two or more variables. When you work with systems of
equations, you can solve them by employing addition and subtraction to elim-
inate variables from the equations on a selective basis. This approach to solving
systems of equations allows you to investigate how to view systems of equations
as matrices. This chapter includes the following topics:
Solving for two variables using substitution
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Using addition and multiplication
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Recognizing no solution and infinite solution scenarios
Solving using different approaches to elimination
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Basic matrices
Extended matrices
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Shared Solutions
As Figure 11.1 illustrates, when two or more equations can generate the same sets
of ordered pairs, they form a system of equations. When you solve a system of
equations, you find sets of values that both equations generate. You can approach
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