Question 28 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is:

(a) 4 (b) 8
(c) 64 (d) 16

Transcript

Question 28 Given that A is a non-singular matrix of order 3 such that A2 = 2A, then value of |2A| is: (a) 4 (b) 8 (c) 64 (d) 16 Given A2 = 2A Taking Determinant both sides |𝑨^𝟐 | = |2𝐴| |𝑨 × 𝑨| = |2𝐴| |𝐴||𝐴| = |𝟐𝑨| Since order of matrix is 3, using|𝑘𝐴|=𝑘^𝑛 |𝐴| |𝐴||𝐴| = 𝟐^𝟑 |𝑨| |𝐴||𝐴| = 8|𝐴| |𝐴||𝐴| − 8|𝐴| = 0 |𝐴| (|𝐴|−"8" ) = 0 Thus, |𝑨| = 0 or |𝑨| = 8 Given that A is a non-singular matrix, ∴ |𝑨| = 8 Now, |𝟐𝑨| = 𝟐^𝟑 |𝑨| = 8 × 8 = 64 So, the correct answer is (C)

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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