Let k be a positive real number and let A B = 2 k − 1 2 k − 2 k 2 k 1 2 k 2 k − 2 k − 1 and = 0 1 − 2 k − k 2 k − 1 0 − 2 k k 2 k 0 If det ( adj A ) + det ( adj

Question

Let k be a positive real number and let A B ​ = ​ 2 k − 1 2 k ​ − 2 k ​ ​ 2 k ​ 1 2 k ​ 2 k ​ − 2 k − 1 ​ ​ and = ​ 0 1 − 2 k − k ​ ​ 2 k − 1 0 − 2 k ​ ​ k ​ 2 k ​ 0 ​ ​ ​ If det ( adj A ) + det ( adj B ) = 1 0 6 , then [ k ] is equal to [Note : adj M denotes the adjoint of a square matrix M and [ k ] denotes the largest integer less than or equal to k ].

TestHub · Accepted Answer

∣ A ∣ = ( 2 k + 1 ) 3 , ∣ B ∣ = 0 But det ( adj A ) = det ( adj B ) = 1 0 6 ​ ⇒ ( 2 k + 1 ) 6 = 1 0 6 ⇒ k = 2 9 ​ ⇒ [ k ] = 4 ​

Mathematics - Determinant Question with Solution | TestHub

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