JEE Main202117 Mar 2021Morning ShiftMathematicsMatricesActual
If A = 2 3 0 - 1 , then the value of det A 4 + det A 10 - ( Adj ( 2 A ) ) 10 is equal to ________.
Correct answer
0
Step-by-step solution
Given, A = 2 3 0 - 1 ⇒ A 2 = 2 3 0 - 1 2 3 0 - 1 = 4 3 0 1 ⇒ A 4 = 4 3 0 1 4 3 0 1 = 16 15 0 1 ⇒ A 5 = 16 15 0 1 2 3 0 - 1 = 32 33 0 - 1 ⇒ A 10 = 32 33 0 - 1 32 33 0 - 1 = 1024 1023 0 1     . . . . i Now, 2 A = 4 6 0 - 2 ⇒ Adj 2 A = - 2 0 - 6 4 T ⇒ Adj 2 A = - 2 - 6 0 4 ⇒ Adj 2 A 2 = - 2 - 6 0 4 - 2 - 6 0 4 = 4 - 12 0 16 ⇒ Adj 2 A 4 = 4 - 12 0 16 4 - 12 0 16 = 16 - 240 0 256 ⇒ Adj 2 A 5 = 16 - 240 0 256 - 2 - 6 0 4 = - 32 - 1056 0 1024 ⇒ Adj 2 A