Exercises display sets in 2. Assume the sets include the

Chapter 2, Problem 1E

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QUESTION:

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.)

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QUESTION:

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.)

ANSWER:

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

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