Problem 1: Let V and W be finite-dimensional vector spaces. a.) Show that the map L(V, W) → L(W', V') given by T→ T' is an isomorphism. b.) Prove that rank T = rank T'. (Note: We proved in class that T → T' is linear. You may use this result.)
Problem 1: Let V and W be finite-dimensional vector spaces. a.) Show that the map L(V, W) → L(W', V') given by T→ T' is an isomorphism. b.) Prove that rank T = rank T'. (Note: We proved in class that T → T' is linear. You may use this result.)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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