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Stitz-Zeager_College_Algebra_e-book

# 3 3 100 120 replace r1 with 2r2 r1 0 1 0 0 0 0 1 0 0

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Unformatted text preview: her an equation which is always true, called an identity, or an equation which is never true, called a contradiction. (If c = 0, then we get 0 = 0, which is always true. If c = 0, then we’d have 0 = 0, which is never true.) Even though identities and contradictions have a large role to play 1 Critics may argue that x = 5 is clearly an equation in one variable. It can also be considered an equation in 117 variables with the coeﬃcients of 116 variables set to 0. As with many conventions in Mathematics, the context will clarify the situation. 450 Systems of Equations and Matrices in the upcoming sections, we do not consider them linear equations. The key to identifying linear equations is to note that the variables involved are to the ﬁrst power and that the coeﬃcients of the variables are numbers. Some examples of equations which are non-linear are x2 + y = 1, xy = 5 and e2x + ln(y ) = 1. We leave it to the reader to explain why these do not satisfy Deﬁnition 8.1. From what we know from Sections 1.2 and 2....
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