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3. Let U and W be subspaces of a vector space V over a field F. Prove that UUW is a subspace of V if and only if UCW or WCU.

3. Let U and W be subspaces of a vector space V over a field F. Prove that UUW is a subspace of V if and only if UCW or WCU.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 34EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 34. ,
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3. Let U and W be subspaces of a vector space V over a field F. Prove that UUW is a subspace of V if and only if UC W or WCU.
Transcribed Image Text:3. Let U and W be subspaces of a vector space V over a field F. Prove that UUW is a subspace of V if and only if UC W or WCU.
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