Prove that if T: V --> W is a linear transformation between the vector space V and the vector space W, then the image of T is a vector subspace of W, and the kernel of T is a vector subspace of V.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 44E: Prove that in a given vector space V, the additive inverse of a vector is unique.
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Prove that if T: V --> W is a linear transformation between the vector space V and the vector space W, then the image of T is a vector subspace of W, and the kernel of T is a vector subspace of V.

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