Show that U = {f € V:|f(x)| ≤k, for some k >0} is a subspace of V, where V = {f: R→ R: f-function } is a vector space on IR with usual operation.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 43E: Prove that in a given vector space V, the zero vector is unique.
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Show that U = {f €V:[f(x)| ≤k, for some k > 0} is a subspace of V, where V =
{f: R→ R:f- function } is a vector space on R with usual operation.
Transcribed Image Text:Show that U = {f €V:[f(x)| ≤k, for some k > 0} is a subspace of V, where V = {f: R→ R:f- function } is a vector space on R with usual operation.
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