Comprehension

निर्देश : निम्नलिखित प्रश्नों के लिए निम्नलिखित को ध्यान में रखें :  

माना \(\rm A=\begin{bmatrix}3&-3&4\\\ 2&-3&4\\\ 0&-1&1\end{bmatrix}\)

A(adj A) किसके बराबर है?

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. \(\rm \begin{bmatrix}5&0&0\\\ 0&5&0\\\ 0&0&5\end{bmatrix}\)
  2. \(\rm \begin{bmatrix}2&0&0\\\ 0&2&0\\\ 0&0&2\end{bmatrix}\)
  3. \(\rm \begin{bmatrix}1/2&0&0\\\ 0&1/2&0\\\ 0&0&1/2\end{bmatrix}\)
  4. \(\rm \begin{bmatrix}1&0&0\\\ 0&1&0\\\ 0&0&1\end{bmatrix}\)

Answer (Detailed Solution Below)

Option 4 : \(\rm \begin{bmatrix}1&0&0\\\ 0&1&0\\\ 0&0&1\end{bmatrix}\)
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Detailed Solution

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व्याख्या:

दिया गया है:

\(\rm A=\begin{bmatrix}3&-3&4\\\ 2&-3&4\\\ 0&-1&1\end{bmatrix} \)

अब, |A| = 3(-3 + 4) -2(-3 + 4) + 0 = 3 - 2 = 1

A(adjA) = |A| I = I

इसलिए, विकल्प (d) सही है।

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