Consider the three following matrices: A=begin{bmatrix}1 & 0&0 0 & -1&00&0&1 end{bmatrix} , B=begin{bmatrix}1 & 0&0 0 & 0&00&0&-1 end{bmatrix} text{ and } C=begin{bmatrix}0 & -i&0 i & 0&-i0&i&0 end{bmatrix} Calculate the Tr(ABC) (a)1 (b)2 (c)2i (d)0

midtlinjeg 2020-10-28 Answered
Consider the three following matrices:
A=[100010001],B=[100000001] and C=[0i0i0i0i0]
Calculate the Tr(ABC)
(a)1
(b)2
(c)2i
(d)0
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Expert Answer

Elberte
Answered 2020-10-29 Author has 95 answers
Step 1
The given matrices are
A=[100010001],B=[100000001] and C=[0i0i0i0i0]
Step 2
Finding the product ABC.
ABC=[100010001][100000001][0i0i0i0i0]
=[100000001][0i0i0i0i0]
=[0i00000i0]
Hence,
ABC=[0i00000i0]
Step 3
Tr(ABC)=sum of the diagonal enteries of the matrix ABC
Tr(ABC)=0+0+0
Tr(ABC)=0
Hence, option d is correct.
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Jeffrey Jordon
Answered 2022-01-30 Author has 2087 answers

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