U = R³ w/ standard vector addition, but w/ scalar multiplication given by r(x, y, z) = (r²x, ry, rz) for (x, y, z) € R³ and r E R. Prove that U is not a vector space by the following distributive property: Let u = vector u For any u € V & real numbers r and s, (r +s) u = ru+su.
U = R³ w/ standard vector addition, but w/ scalar multiplication given by r(x, y, z) = (r²x, ry, rz) for (x, y, z) € R³ and r E R. Prove that U is not a vector space by the following distributive property: Let u = vector u For any u € V & real numbers r and s, (r +s) u = ru+su.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
Related questions
Question
![U = R³ w/ standard vector addition, but w/ scalar multiplication given by r(x, y, z) = (r²x, ry, rz) for (x, y, z)
€ R³ and r E R. Prove that U is not a vector space by the following distributive property:
Let u = vector u
For any u EV & real numbers r and s, (r +s) u = ru+su.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66fa70cb-bd96-49f7-bbde-9ceb23da10ec%2F71f01917-6dc0-4d15-bbf5-d94887de6b6c%2Fv6x5yvf_processed.png&w=3840&q=75)
Transcribed Image Text:U = R³ w/ standard vector addition, but w/ scalar multiplication given by r(x, y, z) = (r²x, ry, rz) for (x, y, z)
€ R³ and r E R. Prove that U is not a vector space by the following distributive property:
Let u = vector u
For any u EV & real numbers r and s, (r +s) u = ru+su.
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
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Algebra and Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305071742/9781305071742_smallCoverImage.gif)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Algebra and Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305071742/9781305071742_smallCoverImage.gif)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning