(c) Let T:V +W be a linear transformation. Prove that if we restrict the domain of T to the orthogonal complement of ker(T), then T: ker(T)- W is one-to-one.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 4CM
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(c) Let T:V + W be a linear transformation. Prove that if we restrict the domain of T to
the orthogonal complement of ker(T), then T: ker(T) W is one-to-one.
Transcribed Image Text:(c) Let T:V + W be a linear transformation. Prove that if we restrict the domain of T to the orthogonal complement of ker(T), then T: ker(T) W is one-to-one.
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