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Question

Let

A+2B=1206-33-531

and

2A-B=2-152-16012

If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A)-Tr(B) has value equal to:


A

0

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B

1

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C

3

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D

2

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Solution

The correct option is D

2


Explanation for the correct option:

Find the value of the given expression.

In the question, two equations are given.

A+2B=1206-33-531...1

2A-B=2-152-16012...2

It is also given that, Tr(A) denotes the sum of all diagonal elements of the matrix A.

Therefore, from equation 1.

trA+2B=-1⇒trA+tr(2B)=-1⇒trA+2tr(B)=-1...3

From equation 2.

tr(2A-B)=3⇒tr(2A)-tr(B)=3⇒2tr(A)-tr(B)=3...4

On solving equation 3 and 4 simultaneously.

We get tr(A)=1 and tr(B)=-1.

So the value of Tr(A)-Tr(B) is 1-(-1)=2.

Therefore, the value of the given expression is 2.

Hence, option D is the correct answer.


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