Problem 5 (Intersections and unions of subspaces) Let V be a vector space. Let U and W be subspaces of V. 1. Show that the intersection UnW is a subspace of V. 2. Show that the union UUW is a subspace of V if and only if either UCW 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.
Problem 5 (Intersections and unions of subspaces) Let V be a vector space. Let U and W be subspaces of V. 1. Show that the intersection UnW is a subspace of V. 2. Show that the union UUW is a subspace of V if and only if either UCW 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
Section4.2: Vector Spaces
Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...
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