Finish the problem the last parts 7.defined asLet A = [a] be a square matrix of size nx n. The trace of A, denoted as Tr(A), isTr(A) = a11 + a22 + a33 +... + ann =nΣa aii.i=1Take 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).

Answered: Image /qna-images/answer/6da2b9a2-0266-4369-85a2-b78cd25aedc3.jpg

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).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

See similar textbooks

Similar questions

Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.
Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]
Find ATA for the matrix A=[531246]. Show that this product is symmetric.
Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.