Let V be a vector space, I the identity operator on V (that is, I(v) = v for all v E V), and Z the zero operator on V (that is, Z(v) = 0y for all v e V). Prove that if W is any subspace of V, then W is invariant under both I and Z.
Let V be a vector space, I the identity operator on V (that is, I(v) = v for all v E V), and Z the zero operator on V (that is, Z(v) = 0y for all v e V). Prove that if W is any subspace of V, then W is invariant under both I and Z.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 24CM
Related questions
Question
100%
![Let V be a vector space, I the identity operator on V (that is, I(v) = v for all v E V),
and Z the zero operator on V (that is, Z(v) = 0y for all v E V). Prove that if W is
any subspace of V, then W is invariant under both I and Z.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb708fa5-116d-42c3-bb62-31dd00678e29%2Fcd92e9e3-1fe5-4417-b34a-d253bcc23f15%2Fx656d5y_processed.png&w=3840&q=75)
Transcribed Image Text:Let V be a vector space, I the identity operator on V (that is, I(v) = v for all v E V),
and Z the zero operator on V (that is, Z(v) = 0y for all v E V). Prove that if W is
any subspace of V, then W is invariant under both I and Z.
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.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
![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
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
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
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning