4. I, Let L: V W be a linear transformation from the vector space V to the vector space W such that kerL = {0}. Suppose the vectors 01, 02, ... , Un in V are linearly independent. Is it true that the vectors L(71), L(2),..., L(Tn) in W must be linearly independent? If it is true, prove it. If it is false, provide an example showing why it is false.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.CR: Review Exercises
Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...
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4.
I, Let L: V W be a linear transformation from the vector space V to
the vector space W such that kerL = {0}. Suppose the vectors 01, 02, ... , Un in V are
linearly independent. Is it true that the vectors L(71), L(2),..., L(Tn) in W must be
linearly independent? If it is true, prove it. If it is false, provide an example showing
why it is false.
Transcribed Image Text:4. I, Let L: V W be a linear transformation from the vector space V to the vector space W such that kerL = {0}. Suppose the vectors 01, 02, ... , Un in V are linearly independent. Is it true that the vectors L(71), L(2),..., L(Tn) in W must be linearly independent? If it is true, prove it. If it is false, provide an example showing why it is false.
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