JEE Main202228 Jul 2022Morning ShiftMathematicsMatricesActual
Let the matrix A = 0 1 0 1 0 0 0 0 1 and the matrix B 0 = A 49 + 2 A 98 . If B n = Adj B n - 1 for all n ≥ 1 , then det B 4 is equal to
Options
- A3 28
- B3 30
- C3 32
- D3 36
Correct answer
C. 3 32
Step-by-step solution
Given A = 0 1 0 1 0 0 0 0 1 Now A 2 = 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 = 1 0 0 0 1 0 0 0 1 = I i.e. A 98 = I ; A 49 = A ∴ B 0 = A 98 + 2 A 49 = I + 2 A = 1 2 0 2 1 0 0 0 3 Given B n = adj B n - 1 ∴ B 4 = adj B 3 = adj adj B 2 = adj adj adj B 1 = adj adj adj adj B 0 ∴ B 4 = B 0 2 4 = B 0 16 Now B 0 = 1 2 0 2 1 0 0 0 3 = - 9 Hence, B 4 = B 0 16 = 9 16 = 3 32