Q3. (25 pts) Let V be a vector space over a field F and X, Y subspaces of V. Is XUY a subspace of V? If yes, prove your argument. If no, give a counter example and then write a proposition which gives necessary and sufficient condition () so that XUY is a subspace of V. Then prove your proposition.
Q3. (25 pts) Let V be a vector space over a field F and X, Y subspaces of V. Is XUY a subspace of V? If yes, prove your argument. If no, give a counter example and then write a proposition which gives necessary and sufficient condition () so that XUY is a subspace of V. Then prove your proposition.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 44EQ
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