The statement is either true in all cases or false. If false, construct a specific example to show that the statement is not always true. If V₁ ..... V4 are in R² and V3 =2v₁ +V₂, then (V₁, V₂, V3, V4} is linearly dependent. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. True. Because V3 = 2v₁ +V₂, V4 must be the zero vector. Thus, the set of vectors is linearly dependent. O B. True. If c₁=2, c₂=1, c3 = 1, and c4 = 0, then c₁v₁ ++C4V4=0. The set of vectors is linearly dependent. O C. True. The vector v3 is a linear combination of v₁ and v₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent. O D. False. If v₁ = V₂ = V3 = C and V4 = then V3 = 2v₁ + V₂ and (V₁ V2 V3 V4) is linearly independent.
The statement is either true in all cases or false. If false, construct a specific example to show that the statement is not always true. If V₁ ..... V4 are in R² and V3 =2v₁ +V₂, then (V₁, V₂, V3, V4} is linearly dependent. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. True. Because V3 = 2v₁ +V₂, V4 must be the zero vector. Thus, the set of vectors is linearly dependent. O B. True. If c₁=2, c₂=1, c3 = 1, and c4 = 0, then c₁v₁ ++C4V4=0. The set of vectors is linearly dependent. O C. True. The vector v3 is a linear combination of v₁ and v₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent. O D. False. If v₁ = V₂ = V3 = C and V4 = then V3 = 2v₁ + V₂ and (V₁ V2 V3 V4) is linearly independent.
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:The statement is either true in all cases or false. If false, construct a specific example to show that the statement is not always true.
If V₁, ..., V4 are in Rª and V3 = 2v₁ +V₂, then {V₁, V₂, V3, V4} is linearly dependent.
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
O A. True. Because V3 = 2v₁ + V₂, V4 must be the zero vector. Thus, the set of vectors is linearly dependent.
O B. True. If c₁=2, c₂=1, c3 = 1, and c = 0, then c₁v₁ ++C₂V4 = 0. The set of vectors is linearly dependent.
O C.
True. The vector v3 is a linear combination of v₁ and v₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
O D.
False. If v₁ =
V₂ =
V3 =
C
and V4 =
then V3 = 2v₁ + V₂ and (V₁ V2 V3 V4} is linearly independent.
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