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Which of the following statements is true about vectors in a vector space V over a field F? A. None of the statements in this list is true. B. A vector v E V is a linear combination of vectors in B if B spans every set of vectors that contain v. OC. A vector v € V is a linear combination of vectors in B C V if v is the sum of all the vectors in B.. O D. A vector v E V is a linear combination of the vectors in B C V if the set of vectors BU {v} is a linearly dependent set of vectors. OE. A vector v € V is called a linear combination of vectors in B C Vif v is

Which of the following statements is true about vectors in a vector space V over a field F? A. None of the statements in this list is true. B. A vector v E V is a linear combination of vectors in B if B spans every set of vectors that contain v. OC. A vector v € V is a linear combination of vectors in B C V if v is the sum of all the vectors in B.. O D. A vector v E V is a linear combination of the vectors in B C V if the set of vectors BU {v} is a linearly dependent set of vectors. OE. A vector v € V is called a linear combination of vectors in B C Vif v is

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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Which of the following statements is true about vectors in a vector space V over a field F? A. None of the statements in this list is true. B. A vector v E V is a linear combination of vectors in B if B spans every set of vectors that contain v. C. A vector ve V is a linear combination of vectors in B C Vif v is the sum of all the vectors in B.. D. A vector v E V is a linear combination of the vectors in B C V if the set of vectors BU {v} is a linearly dependent set of vectors. O E. A vector v E V is called a linear combination of vectors in Bc Vif v is a scalar multiple of at least two vectors in V..
Transcribed Image Text:Which of the following statements is true about vectors in a vector space V over a field F? A. None of the statements in this list is true. B. A vector v E V is a linear combination of vectors in B if B spans every set of vectors that contain v. C. A vector ve V is a linear combination of vectors in B C Vif v is the sum of all the vectors in B.. D. A vector v E V is a linear combination of the vectors in B C V if the set of vectors BU {v} is a linearly dependent set of vectors. O E. A vector v E V is called a linear combination of vectors in Bc Vif v is a scalar multiple of at least two vectors in V..
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