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 ₁V₁ +₂V2 + ... + 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. Op>n ('there are more vectors than entries') = 0 has a nontrivial solution.
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 ₁V₁ +₂V2 + ... + 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. Op>n ('there are more vectors than entries') = 0 has a nontrivial solution.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 19E
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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 ₁V₁ + x₂V2 + ... + pvp
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')
-
O has a nontrivial solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad61a16a-ccb3-4100-87e8-33e1dead9976%2Fa1cfe926-6026-4479-9c36-05f937bc04cb%2F8p0873g_processed.jpeg&w=3840&q=75)
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 ₁V₁ + x₂V2 + ... + pvp
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')
-
O has a nontrivial solution.
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