Let T : R" → R™ be a linear transformation, and let {v1,.., Vp} be a linearly dependent set in R". Show that the set {T(v1), ...,T(v,)} is a linearly dependent set in Rm.

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 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...
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Let T : R" → R" be a linear transformation, and let {v1,..., Vp} be a linearly
dependent set in R". Show that the set {T(v1),...,T(vp)} is a linearly dependent
set in R".
Transcribed Image Text:Let T : R" → R" be a linear transformation, and let {v1,..., Vp} be a linearly dependent set in R". Show that the set {T(v1),...,T(vp)} is a linearly dependent set in R".
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