Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
We have solutions for your book!
See our solution for Question 15E from Chapter 1.7 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 15E
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 system of vectors\[\left[ {\begin{array}{*{20}{l}}5\\1\end{array}} \right],\left[ {\begin{array}{*{20}{l}}2\\8\end{array}} \right],\left[ {\begin{array}{*{20}{l}}1\\3\end{array}} \right],\left[ {\begin{array}{*{20}{c}}{ - 1}\\7\end{array}} \right]\]We have to find whether the given system vectors are linearly dependent or not, just by inspection
Step 1:
We know that if a set of vectors contain more vectors then the number of entries in each vector, then the set is linearly dependent.
In the above case, number of vectors in the set is 4, however, there are only 2 elements in each vector. so the given vectors are not linearly independent.
Not linearly independent
We are given with following system of vectors\[\left[ {\begin{array}{*{20}{l}}5\\1\end{array}} \right],\left[ {\begin{array}{*{20}{l}}2\\8\end{array}} \right],\left[ {\begin{array}{*{20}{l}}1\\3\end{array}} \right],\left[ {\begin{array}{*{20}{c}}{ - 1}\\7\end{array}} \right]\]We have to find whether the given system vectors are linearly dependent or not, just by inspection
Step 1:
We know that if a set of vectors contain more vectors then the number of entries in each vector, then the set is linearly dependent.
In the above case, number of vectors in the set is 4, however, there are only 2 elements in each vector. so the given vectors are not linearly independent.
Not linearly independent