3. Let V be a vector space over R with subspaces U andW.(a) Show that UnW is a subspace of V.(b) Give an example of V, U and W with the prop-erty that UUW is not a subspace of V.(c) Is it true that U \ W = {u € U | u ¢ W} is asubspace of V?

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Answered: 3. Let V be a vector space over R with…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 56E: Give an example showing that the union of two subspaces of a vector space V is not necessarily a...

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3. Let V be a vector space over R with subspaces U and W. (a) Show that U nW is a subspace of V. (b) Give an example of V, U and W with the prop- erty that U UW is not a subspace of V. (c) Is it true that U \ W = {u € U | u ¢ W} is a subspace of V?