Let V={f(x) = R[x] | ƒ(1) = 0, ƒ'(2) = 0}. Here the prime denotes differentiation. Is V a vector space? If so, what is its dimension? Select one: O Yes, and it has dimension 2 O Yes, but it does not have a finite dimension O None of the others apply O Yes, and it has dimension 3 No, it is not a vector space

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...
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Let V={f(x) = R[x] | ƒ(1) = 0, ƒ' (2) = 0}. Here the prime denotes differentiation.
Is V a vector space?
If so, what is its dimension?
Select one:
O Yes, and it has dimension 2
O Yes, but it does not have a finite dimension
None of the others apply
O Yes, and it has dimension 3
O No, it is not a vector space
Transcribed Image Text:Let V={f(x) = R[x] | ƒ(1) = 0, ƒ' (2) = 0}. Here the prime denotes differentiation. Is V a vector space? If so, what is its dimension? Select one: O Yes, and it has dimension 2 O Yes, but it does not have a finite dimension None of the others apply O Yes, and it has dimension 3 O No, it is not a vector space
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