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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
Question
Let $A=\left[\begin{array}{ccc}2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2\end{array}\right]$. If $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} 2 A))|=(16)^{ n }$, then $n$ is equal to
✓

Answer

a
$| A |=2[3]-1[2]=4$

$\therefore|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} 2 A ))|$

$=|2 A |^{( n -1)^3} \Rightarrow|2 A |^8=16^n$

$\Rightarrow\left(2^3|A|\right)^8=16^n$

$\Rightarrow\left(2^3 \times 2^2\right)^8=16^n$

$=2^{40}=16^n$

$=16^{10}=16^n \Rightarrow n=10$

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