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

midtlinjeg

Answered question

2020-10-28

Consider the three following matrices:
A=[100010001],B=[100000001] and C=[0i0i0i0i0]
Calculate the Tr(ABC)
(a)1
(b)2
(c)2i
(d)0

Answer & Explanation

Elberte

Elberte

Skilled2020-10-29Added 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.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-30Added 2605 answers

Answer is given below (on video)

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