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Let V and W be finite-dimensional vector spaces and T: V > W be an isomorphism. Let Vn
Chapter 2, Problem 17(choose chapter or problem)
QUESTION:
Let V and W be finite-dimensional vector spaces and T: V > W be an isomorphism. Let Vn be a subspace of V. (a) Prove that T(V0) is a subspace of W. (b) Prove that dim(V0) = dim(T(V0)
Questions & Answers
QUESTION:
Let V and W be finite-dimensional vector spaces and T: V > W be an isomorphism. Let Vn be a subspace of V. (a) Prove that T(V0) is a subspace of W. (b) Prove that dim(V0) = dim(T(V0)
ANSWER:
Step 1 of 2
Since is an isomorphism, it is one-to –one and onto. Since is a vector subspace of is a vector subspace of W. Moreover both and must be finite dimensional. Now consider the restricted mapping