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Show that if U and W are subspaces of the vector space V, then dim UnW < min{dim U, dim W} . Prove or find a counterexample: If a is a basis for U and 3 is a basis for W, is anß a basis for UnW?

Show that if U and W are subspaces of the vector space V, then dim UnW < min{dim U, dim W} . Prove or find a counterexample: If a is a basis for U and 3 is a basis for W, is anß a basis for UnW?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 22EQ
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Show that if U and W are subspaces of the vector space V, then dim UnW < min{dim U, dim W} Prove or find a counterexample: If a is a basis for U and B is a basis for W, is anB a basis for U nW?
Transcribed Image Text:Show that if U and W are subspaces of the vector space V, then dim UnW < min{dim U, dim W} Prove or find a counterexample: If a is a basis for U and B is a basis for W, is anB a basis for U nW?
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