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
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: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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