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

ધારો કે \(A\) એ એવો \(n \times n\) શ્રેણિક છે કે જેથી \(| A |=2\) પર થાય.જો શ્રેણિક \(\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 A ^{-1}\right)\right) \cdot\) નો  નિશ્ચાયક \(2^{84}\) હોય, તો \(n =.............\).

  1. A \(10\)
  2. B \(12\)
  3. C \(16\)
  4. D \(5\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(5\)

Step-by-step Solution

Detailed explanation

\(\left|\operatorname{Adj}\left(2 Adj \left(2 A ^{-1}\right)\right)\right|\) \(=\left|2 \operatorname{Adj}\left(\operatorname{Adj}\left(2 A ^{-1}\right)\right)\right|^{ n -1}\) \(=2^{n(n-1)}\left|\operatorname{Adj}\left(2 A ^{-1}\right)\right|^{n-1}\)…
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