Let k be a positive real number and let A = [\table 2k-1,2\sqrtk,2\sqrtk;2\sqrtk,1,-2k;-2\sqrtk,2k,-1] and B = [\table 0,2k-1,\sqrtk;1-2k,0,2\sqrtk;-\sqrtk,-2\sqrtk,0]. If det(adj A) + det(adj B) = 10^6, then [k] is equal to _____. (Note: adjM denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k). [JEE Adv 2010 P2]

Matrices and Determinants

Section: Mathematics

Question : 48 of 56

Marks: +1, -0

Let k be a positive real number and let A = [

2k−1	2√k	2√k
2√k	1	−2k
−2√k	2k	−1

] and B = [

0	2k−1	√k
1−2k	0	2√k
−√k	−2√k	0

]. If det(adj A) + det(adj B) = 106, then [k] is equal to _____.
(Note: adjM denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to k).

[JEE Adv 2010 P2]

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