29. Suppose the vectors v, V2, ..., Vr in a vector space V are linearly dependent. Which statement does NOT necessarily follow?: (A) The vectors are not linearly independent (B) There exists a linear relationship among the vectors v1, V2s . .. , Vk k (C) a;v; = 0 = ai 7 0, for at least one i = 1,...k i=l (D) The span of the given vectors equals V (E) Some of the vectors v,, V2, ... , Vr can be written as a linear combination of the other vectors
29. Suppose the vectors v, V2, ..., Vr in a vector space V are linearly dependent. Which statement does NOT necessarily follow?: (A) The vectors are not linearly independent (B) There exists a linear relationship among the vectors v1, V2s . .. , Vk k (C) a;v; = 0 = ai 7 0, for at least one i = 1,...k i=l (D) The span of the given vectors equals V (E) Some of the vectors v,, V2, ... , Vr can be written as a linear combination of the other vectors
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:29. Suppose the vectors v,, V2, ..., Vr in a vector space V are linearly dependent. Which
statement does NOT necessarily follow?:
(A) The vectors are not linearly independent
(B) There exists a linear relationship among the vectors v1, V2s . .. , Vk
(C) a;v; = 0 = a; # 0, for at least one i = 1,...k
i=1
(D) The span of the given vectors equals V
(E) Some of the vectors v1, V2, ... , Vr can be written as a linear combination of the other
vectors
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