The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal e of A. If X and Y are n-by-n matrices, which of the following is a true statement? (b) If tr(X) = 0, then X = On- (d) tr(XY) = tr(YX). (a) tr(X²) = [tr(X)]². (c) tr(XY) = tr(X)tr(Y).
The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal e of A. If X and Y are n-by-n matrices, which of the following is a true statement? (b) If tr(X) = 0, then X = On- (d) tr(XY) = tr(YX). (a) tr(X²) = [tr(X)]². (c) tr(XY) = tr(X)tr(Y).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 10CR
Related questions
Question
![The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal entries
of A. If X and Y are n-by-n matrices, which of the following is a true statement?
(a) tr(X²) = [tr(X)]².
(c) tr(XY) = tr(X)tr(Y).
(b) If tr(X) = 0, then X = On.
(d) tr(XY) = tr(YX).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5d888c4-34df-48d6-9f29-727a3238dd4b%2F14147c66-4f6c-49b5-b2ec-fed7915d519e%2F5ckqgr_processed.png&w=3840&q=75)
Transcribed Image Text:The trace of a square matrix A, denoted by tr(A), is defined as the sum of the main diagonal entries
of A. If X and Y are n-by-n matrices, which of the following is a true statement?
(a) tr(X²) = [tr(X)]².
(c) tr(XY) = tr(X)tr(Y).
(b) If tr(X) = 0, then X = On.
(d) tr(XY) = tr(YX).
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 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781305115545/9781305115545_smallCoverImage.gif)
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
![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
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781305115545/9781305115545_smallCoverImage.gif)
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
![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
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning