7. defined as Let A = [a] be a square matrix of size n x n. The trace of A, denoted as Tr(A), is Tr(A) = a11 + a22+a33 + + ann = n aii. i=1 Take A, B square matrices of size n x 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 n x n. The trace of A, denoted as Tr(A), is Tr(A) = a11 + a22+a33 + + ann = n aii. i=1 Take A, B square matrices of size n x 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
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![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%2F25ff7613-d967-4bfc-8db5-8e2805cacd27%2Fgqkji7g_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).
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Step 1: To find trace of the matrix.
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