1. Tardigrade
  2. Question
  3. Mathematics
  4. 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......

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Q. Let $k$ be a positive real number and let
$A=\begin {bmatrix} 2k-1 & 2\sqrt k & 2\sqrt k \\ 2\sqrt k & 1 & -2k \\ -2\sqrt k & 2k & -1 \end {bmatrix}$ and
$B=\begin {bmatrix} 0 & 2k-1 & \sqrt k \\ 1-2k & 0 & 2\sqrt k \\ -\sqrt k & -2\sqrt k & .0 \end {bmatrix}$
If $det (adj A) + det (adj B) = 10^6$, then $ [k]$ is equal to......

IIT JEEIIT JEE 2010Determinants

Solution:

$| A | = (2k + 1)^3,|B |= 0$
But $det (adj .A) + det (adj B) = 10^6$
$\Rightarrow (2k+1)^6 =10^{6} \Rightarrow k=\frac{9}{2} \Rightarrow [k]=4$