Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
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See our solution for Question 20E from Chapter 1.7 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 20E
Chapter:
Problem:
Determine by inspection whether the vectors in Exercises 15–20 are linearly independent. Justify each answer.
Step-by-Step Solution
Given Information
We are given with following vectors\[\left[ {\begin{array}{*{20}{c}}1\\4\\{ - 7}\end{array}} \right],\left[ {\begin{array}{*{20}{c}}{ - 2}\\5\\3\end{array}} \right],{\rm{ and }}\left[ {\begin{array}{*{20}{l}}0\\0\\0\end{array}} \right]\]We have to determine whether these vectors are linearly independent or not, by inspection.
Step-1:
As we can notice that there is a zero vector in given set, hence the vectors can not be linearly independent Therefore,
Linearly dependent
We are given with following vectors\[\left[ {\begin{array}{*{20}{c}}1\\4\\{ - 7}\end{array}} \right],\left[ {\begin{array}{*{20}{c}}{ - 2}\\5\\3\end{array}} \right],{\rm{ and }}\left[ {\begin{array}{*{20}{l}}0\\0\\0\end{array}} \right]\]We have to determine whether these vectors are linearly independent or not, by inspection.
Step-1:
As we can notice that there is a zero vector in given set, hence the vectors can not be linearly independent Therefore,
Linearly dependent