Let u4 be a vector that is not a linear combination of {u₁, U₂, U3, }. Select the best statement. © A. span{u₁, U₂, U3} = span{u₁, U₂, U3, U4} . B. There is no obvious relationship between span{u₁, u₂, u3} and span{u₁, U₂, U3, U4} . © C. span{u₁, U₂, U3} is a proper subset of span{u₁, U₂, U3, U4 } . © D. span{u₁, U₂, U3} = span{u₁, U₂, U3, U4} when none of {u₁, U₂, U3, } is a linear combination of the others. OE. We only know that span {u₁, U₂, U3} C span{u₁, U₂, U3, U4 ). F. We only know that span{u₁, U₂, U3, U4} C span{u₁, U₂, U3 } . G. none of the above

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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Let u4 be a vector that is not a linear combination of {u₁, U₂, U3, }.
Select the best statement.
© A. span{u₁, U₂, U3 } = span{u₁, U₂, U3, U4 } .
B. There is no obvious relationship between span{u₁, U₂, U3) and span{u₁, U₂, U3, U4} .
© C. span{u₁, U₂, U3} is a proper subset of span{u₁, U₂, U3, U4 } .
© D. span{u₁, U₂, U3 } = span{U₁, U₂, U3, U4} when none of {u₁, U₂, U3, } is a linear combination of the
others.
E. We only know that span{u₁, U₂, U3} C span{u₁, U₂, U3, U4 }.
F. We only know that span{U₁, U₂, U3, U4 } C span{u₁, U₂, U3 } .
OG. none of the above
Transcribed Image Text:Let u4 be a vector that is not a linear combination of {u₁, U₂, U3, }. Select the best statement. © A. span{u₁, U₂, U3 } = span{u₁, U₂, U3, U4 } . B. There is no obvious relationship between span{u₁, U₂, U3) and span{u₁, U₂, U3, U4} . © C. span{u₁, U₂, U3} is a proper subset of span{u₁, U₂, U3, U4 } . © D. span{u₁, U₂, U3 } = span{U₁, U₂, U3, U4} when none of {u₁, U₂, U3, } is a linear combination of the others. E. We only know that span{u₁, U₂, U3} C span{u₁, U₂, U3, U4 }. F. We only know that span{U₁, U₂, U3, U4 } C span{u₁, U₂, U3 } . OG. none of the above
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