JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
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
- A \(10\)
- B \(9\)
- C \(12\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(10\)
Step-by-step Solution
Detailed explanation
\(| A |=2[3]-1[2]=4\) \(\therefore|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} 2 A ))|\) \(=|2 A |^{( n -1)^3} \Rightarrow|2 A |^8=16^n\) \(\Rightarrow\left(2^3|A|\right)^8=16^n\) \(\Rightarrow\left(2^3 \times 2^2\right)^8=16^n\) \(=2^{40}=16^n\)…
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