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Exercises display sets in 2. Assume the sets include the

Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald ISBN: 9780321982384 49

Solution for problem 1E Chapter 2.8

Linear Algebra and Its Applications | 5th Edition

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Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald

Linear Algebra and Its Applications | 5th Edition

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Problem 1E

Problem 1E

Exercises display sets in ℝ2. Assume the sets include the bounding lines. In each case, give a specific reason why the set H is not a subspace of ℝ2. (For instance, find two vectors in H whose sum is not in H, or find a vector in H with a scalar multiple that is not in H. Draw a picture.)

Step-by-Step Solution:
Step 1 of 3

Solution:-

Step1

Given that

Step2

To find

Assume the sets include the bounding lines. In each case, give a specific reason why the set H is not a subspace of ℝ2. (For instance, find two vectors in H whose sum is not in H, or find a vector in H with a scalar multiple that is not in H. Draw a picture.)

Step3

We have

Diagram

Step4

As we can see that v=(1,1) is in given set, but -1.v=(-1,-1) is not in this set.

Step 2 of 3

Chapter 2.8, Problem 1E is Solved
Step 3 of 3

Textbook: Linear Algebra and Its Applications
Edition: 5
Author: David C. Lay; Steven R. Lay; Judi J. McDonald
ISBN: 9780321982384

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Exercises display sets in 2. Assume the sets include the