Misc 19 - Let A = [1 sin 1 -sin 1 sin -1 -sin 1], then - Miscellaneous

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Misc. 19 Choose the correct answer. Let A = 1 sin 1 sin 1 sin 1 sin 1 , where 0 2 , then A. Det (A) = 0 B. Det (A) (2, C. Det (A) (2, 4) D. Det (A) [2, 4] A = 1 sin 1 sin 1 sin 1 sin 1 |A| = 1 sin 1 sin 1 sin 1 sin 1 = 1 1 sin sin 1 sin sin sin 1 1 + 1 sin 1 1 sin = 1 (1 + sin2 ) sin ( sin + sin ) + 1 (sin2 + 1) = 1 (1 + sin2 ) sin (0) + 1(sin2 + 1) = 2 (1 + sin2 ) Thus, |A| = 2 (1 + sin2 ) We know that 1 sin 1 So, value of sin can be from 1 to 1 Suppose, Hence, value of sin2 can be from 0 to 1 (negative not possible) Thus 2 |A| 4 |A| [2 , 4] Det (A) [2 , 4] Thus D is the correct answer

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.