Let V be a vector space over R. Assume that 1, 02, 03 EV are vectors such that V = Span{1, 02, 03}. Prove that V = Span{v1 – 02, T2 – 03, 03}. (Fun fact: You might notice that there's nothing special about 3 vectors - in fact, if V Span{01,..., Un}, then V = Span{v1 – 02, 02 – 03,..., Tn-1 - Un, Tn}!)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let V be a vector space over R. Assume that 01, 02, 03 E V are vectors such that V = Span{01, 02, 03}.
Prove that V = Span{v1 – 02, 02 – 03, 03}.
(Fun fact: You might notice that there's nothing special about 3 vectors
Span{01, ..., Tn}, then V = Span{v1 – 02, 02 – 03, ..., Tn-1 – Un, Un}!)
in fact, if V
Transcribed Image Text:Let V be a vector space over R. Assume that 01, 02, 03 E V are vectors such that V = Span{01, 02, 03}. Prove that V = Span{v1 – 02, 02 – 03, 03}. (Fun fact: You might notice that there's nothing special about 3 vectors Span{01, ..., Tn}, then V = Span{v1 – 02, 02 – 03, ..., Tn-1 – Un, Un}!) in fact, if V
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