

Miscellaneous
Misc. 2 Important Deleted for CBSE Board 2022 Exams
Misc 3
Misc 4 Deleted for CBSE Board 2022 Exams
Misc 5
Misc 6 Important Deleted for CBSE Board 2022 Exams
Misc 7 Important
Misc 8
Misc 9
Misc 10
Misc 11 Important Deleted for CBSE Board 2022 Exams
Misc 12 Important Deleted for CBSE Board 2022 Exams
Misc. 13 Deleted for CBSE Board 2022 Exams
Misc 14 Deleted for CBSE Board 2022 Exams
Misc. 15 Important Deleted for CBSE Board 2022 Exams
Misc. 16 Important
Misc 17 (MCQ) Important Deleted for CBSE Board 2022 Exams
Misc 18 (MCQ)
Misc 19 (MCQ) Important You are here
Matrices and Determinants - Formula Sheet and Summary Important
Last updated at Aug. 9, 2021 by Teachoo
Misc 19 Choose the correct answer. Let A = [■8(1&sinθ&1@−sinθ&1&sinθ@−1&〖−sin〗θ&1)] , where 0 ≤ θ≤ 2π, then A. Det (A) = 0 B. Det (A) ∈ (2, ∞) C. Det (A) ∈ (2, 4) D. Det (A)∈ [2, 4] A = [■8(1&sinθ&1@−sinθ&1&sinθ@−1&〖−sin〗θ&1)] |A| = |■8(1&sinθ&1@−sinθ&1&sinθ@−1&〖−sin〗θ&1)| = 1 |■8(1&sinθ@−sinθ&1)| – sin θ |■8(−sinθ&sinθ@−1&1)| + 1 |■8(−sinθ&1@−1&〖−sin〗θ )| = 1 (1 + sin2 θ) – sin θ (–sin θ + sin θ) + 1 (sin2 θ + 1) = (1 + sin2 θ) –sin θ × 0 + (1 + sin2 θ) = 2 (1 + sin2 θ) Thus, |A| = 2 (1 + sin2 θ) We know that –1 ≤ sin θ ≤ 1 So, value of sin θ can be from –1 to 1 Suppose, Hence, value of sin2 θ 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 sin θ = –1 sin2 θ = 1 sin θ = 1 sin2 θ = 1 sin θ = 0 sin2 θ = 0 Putting sin2 θ = 0 in |A| |A| = 2(1 + 0) |A| = 2 Thus minimum value of |A| is 2 Putting sin2 θ = 1 in |A| |A| = 2 (1 + 1) = 2 (2) = 4 Thus maximum value of |A| is 4