Let `K` be a positive real number and `A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-2k-2sqrt(k)2k-1]a n dB=[0 2k-1sqrt(k)1-2k0 2-sqrt(k)-2sqrt(k)0]` . If det `(a d jA)+det(a d jB)=10^6,t h e n[k]` is equal to. [Note: `a d jM` denotes the adjoint of a square matix `M` and `[k]` denotes the largest integer less than or equal to `K` ].

Answer

4

Explanation

`|A|=(2k+1)^(3), |B|=0` (since B is a skew-symmetric matrix of order 3)
`implies` det (adj A)`=|A|^(n-1)=((2k+1)^(3))^(2)=10^(6)`
`implies 2k+1=10` or `2k=9`
`implies [K]=4`.