Show that the union UUW is a subspace of V if and only if either UC W or W CU. Hint 1: Try a proof by contradiction. Hint 2: Think about the intersection of two non-parallel planes (passing through the origin) in R³ before tackling the general statement.

Show that the union UUW is a subspace of V if and only if either UC W or W CU. Hint 1: Try a proof by contradiction. Hint 2: Think about the intersection of two non-parallel planes (passing through the origin) in R³ before tackling the general statement.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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Question

Intersections and unions of subspaces

Let V be a vector space. Let U and W be subspaces of V.

Show that the union UUW is a subspace of V if and only if either UC W or W CU. Hint 1: Try a
proof by contradiction. Hint 2: Think about the intersection of two non-parallel planes (passing through
the origin) in R³ before tackling the general statement.

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