Answered: 2. Is H closed under addition? If it…

2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and syntax such as <1,2>, <3,4>. <6,0>

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 41CR: Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the...

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Chapter 3.2 Question 3

What is the answer to part 2, everything else is answered correctly.

Let V = R? and let H be the subset of V of all points on the line -4x + 3y = -12. Is H a subspace of the vector space V?
1. Is H nonempty?
H is nonempty v O
2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H, using a comma separated list and syntax such
as <1,2>, <3,4>.
< 6,0>
3. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in R and a vector in H whose product is not in H, using a comma
separated list and syntax such as 2, <3,4>.
2, < 3,0 >
4. Is H a subspace of the vector space V? You should be able to justify your answer by writing a complete, coherent, and detailed proof based on your
answers to parts 1-3.
H is not a subspace of V v O

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