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Which of the following is a necessary condition for a set of vectors {V1, V2, ..., Vp} in R" to be linearly dependent? In other words, if all you know is that {V1, V2, ..., conditions must be true? ,Vp) is a linearly dependent set, which of the following The equation ₁V₁ + x2V₂ + ... + XpVp O has a nontrivial solution. One of the vectors is a linear combination of the other vectors. One of the vectors is the zero vector. One of the vectors is a multiple of one of the other vectors. Op>n ('there are more vectors than entries')

Which of the following is a necessary condition for a set of vectors {V1, V2, ..., Vp} in R" to be linearly dependent? In other words, if all you know is that {V1, V2, ..., conditions must be true? ,Vp) is a linearly dependent set, which of the following The equation ₁V₁ + x2V₂ + ... + XpVp O has a nontrivial solution. One of the vectors is a linear combination of the other vectors. One of the vectors is the zero vector. One of the vectors is a multiple of one of the other vectors. Op>n ('there are more vectors than entries')

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 is a necessary condition for a set of vectors {V₁, V2, ..., Vp} in R" to be linearly dependent? In other words, if all you know is that {V1, V2, ..., Vp} is a linearly dependent set, which of the following conditions must be true? The equation X₁V₁ + x₂V₂ + ... + XpVp One of the vectors is a linear combination of the other vectors. One of the vectors is the zero vector. One of the vectors is a multiple of one of the other vectors. p> n ('there are more vectors than entries') = 0 has a nontrivial solution.
Transcribed Image Text:Which of the following is a necessary condition for a set of vectors {V₁, V2, ..., Vp} in R" to be linearly dependent? In other words, if all you know is that {V1, V2, ..., Vp} is a linearly dependent set, which of the following conditions must be true? The equation X₁V₁ + x₂V₂ + ... + XpVp One of the vectors is a linear combination of the other vectors. One of the vectors is the zero vector. One of the vectors is a multiple of one of the other vectors. p> n ('there are more vectors than entries') = 0 has a nontrivial solution.
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