Explain why the vectors u₁ = (2, 4,-4) U₂ = (-4,-8, 8) form a linearly dependent set of vectors in R³. (Solve this problem by inspection.) O The given vectors form a linearly dependent set since they are expressible as a linear combination of the standard basis vectors. O The given vectors form a linearly dependent set since U₁ + U₂ = U₂ + U₁. O The given vectors form a linearly dependent set since any two vectors in R³ form a linearly dependent set. O The given vectors form a linearly dependent set since u₁ + U₂ = (-2,-4, 4). O The given vectors form a linearly dependent set since u₂ = -2 u₁.
Explain why the vectors u₁ = (2, 4,-4) U₂ = (-4,-8, 8) form a linearly dependent set of vectors in R³. (Solve this problem by inspection.) O The given vectors form a linearly dependent set since they are expressible as a linear combination of the standard basis vectors. O The given vectors form a linearly dependent set since U₁ + U₂ = U₂ + U₁. O The given vectors form a linearly dependent set since any two vectors in R³ form a linearly dependent set. O The given vectors form a linearly dependent set since u₁ + U₂ = (-2,-4, 4). O The given vectors form a linearly dependent set since u₂ = -2 u₁.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![Explain why the vectors
u₁ = (2, 4,-4)
U₂ = (-4,-8, 8)
form a linearly dependent set of vectors in R³.
(Solve this problem by inspection.)
O The given vectors form a linearly
dependent set since they are
expressible as a linear combination of
the standard basis vectors.
O The given vectors form a linearly
dependent set since U₁ + U₂ = U₂ + U₁.
O The given vectors form a linearly
dependent set since any two vectors in
R³ form a linearly dependent set.
O The given vectors form a linearly
dependent set since u₁ + U₂ = (-2,-4, 4).
O The given vectors form a linearly
dependent set since u₂ = -2 u₁.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89f8dde5-ac6b-477a-aa58-3cd262523994%2F62d6874e-0ce4-4e75-87f3-8f49421c2b99%2F00bsjz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Explain why the vectors
u₁ = (2, 4,-4)
U₂ = (-4,-8, 8)
form a linearly dependent set of vectors in R³.
(Solve this problem by inspection.)
O The given vectors form a linearly
dependent set since they are
expressible as a linear combination of
the standard basis vectors.
O The given vectors form a linearly
dependent set since U₁ + U₂ = U₂ + U₁.
O The given vectors form a linearly
dependent set since any two vectors in
R³ form a linearly dependent set.
O The given vectors form a linearly
dependent set since u₁ + U₂ = (-2,-4, 4).
O The given vectors form a linearly
dependent set since u₂ = -2 u₁.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning