Let k be a positive real number and let aligned A & = [ array ccc 2 k-1 & 2 k & 2 k 2 k & 1 & -2 k -2 k & 2 k & -1 array ] and B & = [ array ccc 0 & 2 k-1 & k 1-2 k & 0 & 2 k - k & -2 k & 0 array ] aligned If det ( adj A)+ det ( adj B)=10^6

Question

Let k be a positive real number and let aligned A & = [ array ccc 2 k-1 & 2 k & 2 k 2 k & 1 & -2 k -2 k & 2 k & -1 array ] and B & = [ array ccc 0 & 2 k-1 & k 1-2 k & 0 & 2 k - k & -2 k & 0 array ] aligned If det ( adj A)+ det ( adj B)=10^6 , 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 ].

Quantrex Academy · Accepted Answer

Correct answer: 0

|A|=(2 k+1)^3,|B|=0 But det ( adj A)= det ( adj B)=10^6 aligned & (2 k+1)^6=10^6 & k= 9 2 [k]=4 aligned

Correct answer

Step-by-step solution

More from Determinants