This question is from a first year linear algebra course: Let V,W be two subspaces of Rn. . Prove that the intersection V ∩ W is also a subspace: . Prove that the union V ∪ W is a subspace exactly like V ⊆ W or W ⊆ V: (not a proper subset)

This question is from a first year linear algebra course: Let V,W be two subspaces of Rn. . Prove that the intersection V ∩ W is also a subspace: . Prove that the union V ∪ W is a subspace exactly like V ⊆ W or W ⊆ V: (not a proper subset)

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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Question

This question is from a first year linear algebra course: Let V,W be two subspaces of Rⁿ.

. Prove that the intersection V ∩ W is also a subspace:

. Prove that the union V ∪ W is a subspace exactly like V ⊆ W or W ⊆ V: (not a proper subset)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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