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: Show that there are no nxn matrices A and B such that AB – BA= In. & You may cite, without proving, any of the properties of the trace function recorded in Problem 4 of Homework 1.

: Show that there are no nxn matrices A and B such that AB – BA= In. & You may cite, without proving, any of the properties of the trace function recorded in Problem 4 of Homework 1.

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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Trese, problem 4 is for reference

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) = > aji. 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) (iii) Tr(AB) = Tr(BA) (iv) Tr(A") = Tr(A) (v) Tr(A" A) > 0
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) = > aji. 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) (iii) Tr(AB) = Tr(BA) (iv) Tr(A") = Tr(A) (v) Tr(A" A) > 0
Show that there are no nxn matrices A and B such that AB – BA = In. & You may cite, without proving, any of the properties of the trace function recorded in Problem 4 of Homework 1.
Transcribed Image Text:Show that there are no nxn matrices A and B such that AB – BA = In. & You may cite, without proving, any of the properties of the trace function recorded in Problem 4 of Homework 1.
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