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 - Page 11: 68


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

Work Step by Step

(a) This is false. If we look at the geometrical interpretation, the intersection can occur (if it occurs) either at a single point or at infinitely many points (for example in a line) but it can never occur at two isolated points. (b) This is true by definition of equivalence of two system of linear equations. (c) This is false. For example the system \begin{align*} x+y=3\\ x-y=1\\ 2x-3y = 1 \end{align*} has the solution $x=2$ and $y=1$.
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