20 Prove the Rank-Nullity Theorem (Theorem 3.35) in the case that ker T = (0).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 13EQ
Related questions
Question
Exercise 3.4.20
Don't copy from any other account
![rank A¹ < r = rank A.
(c) Use the above fact to give another proof of Theorem 3.34.
3.4.20 Prove the Rank-Nullity Theorem (Theorem 3.35) in the case that
ker T = (0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F572394d6-763b-4634-a070-d7c873f29a55%2F3cb45b9c-99ea-425f-829a-5b00b4361171%2F8gq62s4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:rank A¹ < r = rank A.
(c) Use the above fact to give another proof of Theorem 3.34.
3.4.20 Prove the Rank-Nullity Theorem (Theorem 3.35) in the case that
ker T = (0).
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 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![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
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
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
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
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 for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)