Let V be the vector space of all functions from the real field R into R. Show that the set W = {f: f(7) = 2 + f(1)} is not a subspace of V.
Let V be the vector space of all functions from the real field R into R. Show that the set W = {f: f(7) = 2 + f(1)} is not a subspace of V.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Let V be the
the real field R into R. Show that the set
W={f:f(7)=2+f(1)} is not a subspace
of V.
![Let V be the vector space of all functions from
the real field R into R. Show that the set
W = {f: f(7) = 2 + f(1)} is not a subspace
of V.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4031cc9-90e5-40b0-a30e-ae3fc7299b5f%2F8342c634-ebad-4332-813b-0504eec652a9%2F83x23xh_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be the vector space of all functions from
the real field R into R. Show that the set
W = {f: f(7) = 2 + f(1)} is not a subspace
of V.
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