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Let u4 be a linear combination of {u₁, U2, u3}. Select the best statement. ● A. {U₁, U2, U3, U4} is a linearly dependent set of vectors unless one of {u₁, U2, u3} is the zero vector. ● B. {U₁, U2, U3, U4} is never a linearly dependent set of vectors. ● C. {U₁, U2, U3, u4} could be a linearly dependent or lin- early dependent set of vectors depending on the vectors chosen. ● D. {U₁, U2, U3, U4} is always a linearly dependent set of vectors. ● E. {U₁, U2, U3, U4} could be a linearly dependent or lin- early dependent set of vectors depending on the vector space chosen. . F. none of the above

Let u4 be a linear combination of {u₁, U2, u3}. Select the best statement. ● A. {U₁, U2, U3, U4} is a linearly dependent set of vectors unless one of {u₁, U2, u3} is the zero vector. ● B. {U₁, U2, U3, U4} is never a linearly dependent set of vectors. ● C. {U₁, U2, U3, u4} could be a linearly dependent or lin- early dependent set of vectors depending on the vectors chosen. ● D. {U₁, U2, U3, U4} is always a linearly dependent set of vectors. ● E. {U₁, U2, U3, U4} could be a linearly dependent or lin- early dependent set of vectors depending on the vector space chosen. . F. none of the above

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
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Let u4 be a linear combination of {u₁, U2, U3}. Select the best statement. ● A. {u₁, U2, U3, U4} is a linearly dependent set of vectors unless one of {u₁, U2, U3} is the zero vector. ● B. {U1, U2, U3, U4} is never a linearly dependent set of vectors. ● C. {U1, U2, U3, u4} could be a linearly dependent or lin- early dependent set of vectors depending on the vectors chosen. ● D. {U1, U2, U3, u4} is always a linearly dependent set of vectors. ● E. {U1, U2, U3, U4} could be a linearly dependent or lin- early dependent set of vectors depending on the vector space chosen. ● F. none of the above
Transcribed Image Text:Let u4 be a linear combination of {u₁, U2, U3}. Select the best statement. ● A. {u₁, U2, U3, U4} is a linearly dependent set of vectors unless one of {u₁, U2, U3} is the zero vector. ● B. {U1, U2, U3, U4} is never a linearly dependent set of vectors. ● C. {U1, U2, U3, u4} could be a linearly dependent or lin- early dependent set of vectors depending on the vectors chosen. ● D. {U1, U2, U3, u4} is always a linearly dependent set of vectors. ● E. {U1, U2, U3, U4} could be a linearly dependent or lin- early dependent set of vectors depending on the vector space chosen. ● F. none of the above
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