JEE Main202118 Mar 2021Morning ShiftMathematicsMatricesActual
Let A + 2 B = 1 2 0 6 - 3 3 - 5 3 1 and 2 A - B = 2 - 1 5 2 - 1 6 0 1 2 . If T r A denotes the sum of all diagonal elements of the matrix A , then Tr ( A ) - Tr ( B ) has value equal to
Options
- A1
- B2
- C0
- D3
Correct answer
B. 2
Step-by-step solution
A + 2 B = 1 2 0 6 - 3 3 - 5 3 1   … 1 2 A - B = 2 - 1 5 2 - 1 6 0 1 2 ⇒ 4 A - 2 B = 4 - 2 10 4 - 2 12 0 2 4   … 2 1 + 2 ⇒ 5   A = 5 0 10 10 - 5 15 - 5 5 5 A = 1 0 2 2 - 1 3 - 1 1 1 and 2 A = 2 0 4 4 - 2 6 - 2 2 2 ∴ B = 2 0 4 4 - 2 6 - 2 2 2 - 2 - 1 5 2 - 1 6 0 1 2 B = 0 1 - 1 2 - 1 0 - 2 1 0 tr ( A ) = 1 - 1 + 1 = 1 tr ( B ) = - 1 tr ( A ) = 1 and tr ( B ) = - 1 ∴ tr ( A ) - tr ( B ) = 2