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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant

माना \(\mathrm{A}=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]\) और \(\mathrm{B}=\mathrm{I}+\operatorname{adj}(\mathrm{A})+(\operatorname{adj} \mathrm{A})^2+\ldots+\) \((\operatorname{adj} \mathrm{A})^{10}\) है। तो, आव्यूह \(B\) के सभी अवयवों का योग ........... है।

  1. A \(-110\)
  2. B \(22\)
  3. C \(-88\)
  4. D \(-124\)
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Answer & Solution

Correct Answer

(C) \(-88\)

Step-by-step Solution

Detailed explanation

\(\operatorname{Adj}(\text A )=\left[\begin{array}{cc}1 & -2 \\ 0 & 1\end{array}\right]\) \((\operatorname{Adj}\text A)^2=\left[\begin{array}{cc}1 & -4 \\ 0 & 1\end{array}\right]\) \((\operatorname{Adj}\text A)^{10}=\left[\begin{array}{cc}1 & -20 \\ 0 & 1\end{array}\right]\)…
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