7. defined as Let A = [a] be a square matrix of size nx n. The trace of A, denoted as Tr(A), is n =Σa i=1 Tr(A) = a11 + a22+a33 + + ann = aii. Take A, B square matrices of size nx n. Show that (i) Tr(A + B) = Tr(A) + Tr(B); (ii) Tr(AT) = Tr(A); (iii) Tr(AA) = XTr(A), where A is a nozero scalar; (iv) Tr(AB) = Tr(BA).
7. defined as Let A = [a] be a square matrix of size nx n. The trace of A, denoted as Tr(A), is n =Σa i=1 Tr(A) = a11 + a22+a33 + + ann = aii. Take A, B square matrices of size nx n. Show that (i) Tr(A + B) = Tr(A) + Tr(B); (ii) Tr(AT) = Tr(A); (iii) Tr(AA) = XTr(A), where A is a nozero scalar; (iv) Tr(AB) = Tr(BA).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Finish the problem the last parts
![7.
defined as
Let A = [a] be a square matrix of size nx n. The trace of A, denoted as Tr(A), is
Tr(A) = a11 + a22 + a33 +... + ann =
n
Σa aii.
i=1
Take A, B square matrices of size n × n. Show that (i) Tr(A + B) = Tr(A) + Tr(B); (ii) Tr(AT) =
Tr(A); (iii) Tr(\A) = \Tr(A), where X is a nozero scalar; (iv) Tr(AB) = Tr(BA).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd197d1d3-165d-4a29-b5e3-98e832377a62%2F6da2b9a2-0266-4369-85a2-b78cd25aedc3%2Fn34pw8j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.
defined as
Let A = [a] be a square matrix of size nx n. The trace of A, denoted as Tr(A), is
Tr(A) = a11 + a22 + a33 +... + ann =
n
Σa aii.
i=1
Take A, B square matrices of size n × n. Show that (i) Tr(A + B) = Tr(A) + Tr(B); (ii) Tr(AT) =
Tr(A); (iii) Tr(\A) = \Tr(A), where X is a nozero scalar; (iv) Tr(AB) = Tr(BA).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1: Introduction to given details
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)