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Assume 4 is not a linear combination of {u₁, U₂, U3}. Select the best statement. ○ A. {U₁, U₂, U3, U4} is a linearly dependent set precisely when {1₁, 1₂, 13} is a linearly dependent set. ○ B. {U₁, U₂, U3, U₁} could be a linearly independent or linearly dependent set of vectors depending on the vector space chosen ○C. {U₁, U₂, U3, U₁} is never a linearly dependent set of vectors. OD. {1₁, 12, 13, 14} is always a linearly dependent set of vectors. ○E. {U₁, U₂, U3, U4} is a linearly independent set of vectors unless one of {1₁, 12, 13} is the zero vector. OF. none of the above

Assume 4 is not a linear combination of {u₁, U₂, U3}. Select the best statement. ○ A. {U₁, U₂, U3, U4} is a linearly dependent set precisely when {1₁, 1₂, 13} is a linearly dependent set. ○ B. {U₁, U₂, U3, U₁} could be a linearly independent or linearly dependent set of vectors depending on the vector space chosen ○C. {U₁, U₂, U3, U₁} is never a linearly dependent set of vectors. OD. {1₁, 12, 13, 14} is always a linearly dependent set of vectors. ○E. {U₁, U₂, U3, U4} is a linearly independent set of vectors unless one of {1₁, 12, 13} is the zero vector. OF. none of the above

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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Assume 4 is not a linear combination of {u₁, U₂, U3}. Select the best statement. ○ A. {U₁, U₂, U3, U4} is a linearly dependent set precisely when {1₁, 1₂, 13} is a linearly dependent set. ○ B. {U₁, U₂, U3, U₁} could be a linearly independent or linearly dependent set of vectors depending on the vector space chosen. ○C. {U₁, U₂, U3, U₁} is never a linearly dependent set of vectors. OD. {1₁, 12, 13, 14} is always a linearly dependent set of vectors. ○E. {U₁, U₂, U3, U4} is a linearly independent set of vectors unless one of {1₁, 12, 13} is the zero vector. OF. none of the above
Transcribed Image Text:Assume 4 is not a linear combination of {u₁, U₂, U3}. Select the best statement. ○ A. {U₁, U₂, U3, U4} is a linearly dependent set precisely when {1₁, 1₂, 13} is a linearly dependent set. ○ B. {U₁, U₂, U3, U₁} could be a linearly independent or linearly dependent set of vectors depending on the vector space chosen. ○C. {U₁, U₂, U3, U₁} is never a linearly dependent set of vectors. OD. {1₁, 12, 13, 14} is always a linearly dependent set of vectors. ○E. {U₁, U₂, U3, U4} is a linearly independent set of vectors unless one of {1₁, 12, 13} is the zero vector. OF. none of the above
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