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) =...

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

Extracted 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)

Jun 04, 2022

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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) =...

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