Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 1 - Systems of Linear Equations - 1.1 Introduction to Systems of Linear Equations - 1.1 Exercises: 67

Answer

(a) True (b) False (c) False

Work Step by Step

(a) This is true and we can always solve it by equating one of the variables with arbitrary parameter $t$ and express the other variable in terms of $t$ and those expressions will list all of the possible solutions. (b) This is not true. The two equations may not be consistent with each other. Let us show this by example. Consider the system \begin{align*} x+y+z=&5\\ x+y+z=&6 \end{align*} This system is inconsistent because since left sides are equal, right sides have to be also but obviously $5\neq 6$. (c) This is false. The system can also have unique solution.
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