Let K be a positive real number and A=[2...

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` ].

Verified by Experts

`|A| = (2k +1)^(3), |B| = 0`
But det (adj A) + det(adj B) =`10^(6)`
`rArr (2k + 1)^(6) = 10^(6)`
`rArr k = (9)/(2) rArr |k| = 4`

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