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Ex 3.3
Ex 3.3, 2
Ex 3.3, 3
Ex 3.3, 4 Important
Ex 3.3, 5 (i)
Ex 3.3, 5 (ii)
Ex 3.3, 6 (i)
Ex 3.3, 6 (ii) Important
Ex 3.3, 7 (i)
Ex 3.3, 7 (ii) Important
Ex 3.3, 8
Ex 3.3, 9
Ex 3.3, 10 (i) Important
Ex 3.3, 10 (ii)
Ex 3.3, 10 (iii) Important
Ex 3.3, 10 (iv)
Ex 3.3, 11 (MCQ) Important
Ex 3.3, 12 (MCQ) You are here
Last updated at March 16, 2023 by Teachoo
Ex 3.3, 12 If A = [■8(cos 𝛼&〖−sin〗𝛼@sin𝛼&cos𝛼 )] , then A + A’ = I , if the value of α is A. 𝛑/𝟔 B. 𝛑/𝟑 C. π D. 𝟑𝛑/𝟐 A = [■8(cos𝛼&〖−sin〗𝛼@sin𝛼&cos𝛼 )] A’= [■8(cos𝛼&sin𝛼@〖−sin〗𝛼&cos𝛼 )] and I = [■8(1&[email protected]&1)] Given A + A’ = I [■8(cos𝛼&〖−sin〗𝛼@sin𝛼&cos𝛼 )] + [■8(cos𝛼&sin𝛼@〖−sin〗𝛼&cos𝛼 )] = [■8(1&[email protected]&1)] [■8(cos〖𝛼+cos𝛼 〗&〖−sin〗〖𝛼+sin𝛼 〗@sin𝛼 〖−sin〗𝛼&cos〖𝛼+cos𝛼 〗 )]= [■8(1&[email protected]&1)] [■8(2cos𝛼&[email protected]&2cos𝛼 )]= [■8(1&[email protected]&1)] Since the matrices are equal, corresponding elements are equal 2cos 𝛼 = 1 cos𝛼 = 1/2 cos𝛼 = cos〖60°〗 Comparing angles 𝛼 = 60° 𝛼 = 60° × 𝜋/(180°) 𝛼 = 𝜋/3 So the correct answer is (B) (As 𝑐𝑜𝑠〖60°〗= 1/2)