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
icon
Related questions
Question
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.
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning