CBSE Class 12 Sample Paper for 2024 Boards

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Question 13 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

Given that A is a square matrix of order 3 and |A|=- 2 , then |adj( 2 A)| is equal to

a) -2^6                 (b) +4                 (c) -2^8                (d) 2^8

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Transcript

We know that |𝒂𝒅𝒋 𝑨| = |𝑨|^(𝒏−𝟏) where n is the order of determinant ∴|𝒂𝒅𝒋 𝟐𝑨| = |𝟐𝑨|^(𝒏−𝟏) Given Order = n = 3 Now, our equation becomes |𝒂𝒅𝒋 𝟐𝑨| = |𝟐𝑨|^(𝟑−𝟏) |𝑎𝑑𝑗 2𝐴| = |2A|^2 Using property: |𝐤𝑨|=𝒌^𝒏 |𝑨|, Where n is the order of matrix |𝑎𝑑𝑗 2𝐴| = (〖𝟐^𝟑 |𝑨|)〗^𝟐 |𝑎𝑑𝑗 2𝐴| = 〖〖〖(2〗^3)〗^2 |A|〗^2 |𝒂𝒅𝒋 𝟐𝑨| = 𝟐^𝟔 〖(−𝟐)〗^𝟐 |𝑎𝑑𝑗 2𝐴| = 2^6 〖(2)〗^2 |𝒂𝒅𝒋 𝟐𝑨| = 𝟐^𝟖 So, the correct answer is (d)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo