Let A + 2B = [, [6, -3, 3], [-5, 3, 1]] and 2A - B = [[2, -1, 5], [2, -1, 6],]. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) – Tr(B) has value equal to:

Option 1 - 1

Option 2 - 2

Option 3 - 3

Option 4 - 0

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Answered by

Vishal Baghel | Contributor-Level 10

5 months ago

Correct Option - 2

Detailed Solution:

Given the equations:
t? (A + 2B) = -1 which expands to t? (A) + 2t? (B) = -1 . (I)
t? (2A - B) = 3 which expands to 2t? (A) - t? (B) = 3 . (II)

Solving equations (I) and (II) simultaneously, we get:
t? (A) = 1
t? (B) = -1

Therefore, t? (A) - t? (B) = 1 - (-1) = 2.

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