Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 0-32198-238-X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.1 Exercises - Page 11: 23

Answer

a. True. b. False. c. False. d. True.

Work Step by Step

a. The text states this clearly in the paragraph beginning on the bottom of page 6. b. On page 4, the text states that if $m$ and $n$ are positive integers, then an $m\times n$ matrix has $m$ rows and $n$ columns. Hence, a $5\times 6$ matrix has six columns, not rows. c. On page 3, the text states that the set of all possible solutions is called the solution set of the linear system. Hence, a list of numbers $(s_{1},...,s_{n})$ as described is a single solution, but not the solution set. The solution set is the set of all such lists of numbers, of which (cf. pg. 4) there may be none, just one, or infinitely many. d. This comes directly from the box on page 7.
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