1. Let T: VW be a linear map. Let (v₁,...,Un} be a list of n vectors in V. Prove that if the vectors are independent, then U₁,..., Un are also independent. T(v₁),...,T(vn)
1. Let T: VW be a linear map. Let (v₁,...,Un} be a list of n vectors in V. Prove that if the vectors are independent, then U₁,..., Un are also independent. T(v₁),...,T(vn)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Let T: VW be a linear map. Let {v₁,..., Un} be a list of n vectors in V. Prove that if the vectors
T(v₁),..., T(vn) are independent, then v₁,..., Un are also independent.
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