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Consider a linear transformation T: V -> W between vector spaces V and W. Prove that if the kernel (null space) of T is trivial, i.e., {0}, then T is injective (one-to-one).

Consider a linear transformation T: V -> W between vector spaces V and W. Prove that if the kernel (null space) of T is trivial, i.e., {0}, then T is injective (one-to-one).

Elementary Linear Algebra (MindTap Course List)
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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Consider a linear transformation T: V -> W between vector spaces V and W. Prove that if the kernel (null space) of T is trivial, i.e., {0}, then T is injective (one-to-one).

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