Let T be a linear transformation of a vector space V. Prove that{v ∈ V | T(v) = 0}, the kernel of T, is a subspace of V.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.3: Matrices For Linear Transformations
Problem 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
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Let T be a linear transformation of a vector space V. Prove that
{v ∈ V | T(v) = 0}, the kernel of T, is a subspace of V.

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