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Problem 4. If A = aij is an nxn matrix, then the trace of A, Tr(A), is defined as the sum of all the elements on the main diagonal of A, i.e., Tr(A) = >aii. Show each of the following: (i) Tr(aA) = a Tr(A), for each a ER (ii) Tr(A+ B) = Tr(A) + Tr(B)

Problem 4. If A = aij is an nxn matrix, then the trace of A, Tr(A), is defined as the sum of all the elements on the main diagonal of A, i.e., Tr(A) = >aii. Show each of the following: (i) Tr(aA) = a Tr(A), for each a ER (ii) Tr(A+ B) = Tr(A) + Tr(B)

Advanced Engineering Mathematics
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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Problem 4. If A = |aij is an nxn matrix, then the trace of A, Tr(A), defined as the sum of all the elements on the main diagonal of A, i.e., Tr(A) = ) ajj. Show each of the following: i=1 (i) Tr(aA) = a Tr(A), for each a ER (ii) Tr(A+ B) = Tr(A) + Tr(B)
Transcribed Image Text:Problem 4. If A = |aij is an nxn matrix, then the trace of A, Tr(A), defined as the sum of all the elements on the main diagonal of A, i.e., Tr(A) = ) ajj. Show each of the following: i=1 (i) Tr(aA) = a Tr(A), for each a ER (ii) Tr(A+ B) = Tr(A) + Tr(B)
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