Question 10 - 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 Teachoo

The value of |A|, if A=[0 2x-1 √x 1-2x 0 2√x -√x -2√x 0)], where x∈R^+, is

(a) (2x+1)^2 (b) 0 (c) (2x+1)^3 (d) (2x-1)^2

Transcript

Given 𝐴=[■(0&2𝑥−1&√𝑥@1−2𝑥&0&2√𝑥@−√𝑥&−2√𝑥&0)] Since diagonal elements are 0, this might be a skew symmetric matrix Let’s check Finding 𝑨^𝑻 𝐴^𝑇=[■(0&1−2𝑥&−√𝑥@2𝑥−1&0&−2√𝑥@√𝑥&2√𝑥&0)] 𝐴^𝑇=−[■(0&2𝑥−1&√𝑥@1−2𝑥&0&2√𝑥@−√𝑥&−2√𝑥&0)] 𝑨^𝑻= − A Since 𝐴^𝑇= −A ∴ A is a skew symmetric matrix of order 3 We know that , Determinant of every skew symmetric matrix of odd order is 0. ∴ |A| = 0 So, the correct answer is (b)

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Davneet Singh

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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