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3-13. Define the following vectors in R³: e1 = 0 " e2 = " e3 = (a) If v € R³ is an arbitrary vector, write down the linear system which addresses whether v is a linear combination of {e₁,e2, е3}. (b) Show that for any vector v € R³, we can write v as a linear combination of {e₁,e2, е3}.

3-13. Define the following vectors in R³: e1 = 0 " e2 = " e3 = (a) If v € R³ is an arbitrary vector, write down the linear system which addresses whether v is a linear combination of {e₁,e2, е3}. (b) Show that for any vector v € R³, we can write v as a linear combination of {e₁,e2, е3}.

Advanced Engineering Mathematics
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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3-13. Define the following vectors in R³: e₁ = H. e2 1 - 9 e3 0 - (a) If v € R³ is an arbitrary vector, write down the linear system which addresses whether v is a linear combination of {e₁,e2, е3}. (b) Show that for any vector v € R³, we can write v as a linear combination of {e₁,e2, е3}.
Transcribed Image Text:3-13. Define the following vectors in R³: e₁ = H. e2 1 - 9 e3 0 - (a) If v € R³ is an arbitrary vector, write down the linear system which addresses whether v is a linear combination of {e₁,e2, е3}. (b) Show that for any vector v € R³, we can write v as a linear combination of {e₁,e2, е3}.
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