Ex 3.3

Chapter 3 Class 12 Matrices
Serial order wise

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### Transcript

Ex 3.3, 12 If A = [■8(cos 𝛼&〖−sin〗⁡𝛼@sin⁡𝛼&cos⁡𝛼 )] , then A + A’ = I , if the value of α is A. 𝛑/𝟔 B. 𝛑/𝟑 C. π D. 𝟑𝛑/𝟐 A = [■8(cos⁡𝛼&〖−sin〗⁡𝛼@sin⁡𝛼&cos⁡𝛼 )] A’= [■8(cos⁡𝛼&sin⁡𝛼@〖−sin〗⁡𝛼&cos⁡𝛼 )] and I = [■8(1&[email protected]&1)] Given A + A’ = I [■8(cos⁡𝛼&〖−sin〗⁡𝛼@sin⁡𝛼&cos⁡𝛼 )] + [■8(cos⁡𝛼&sin⁡𝛼@〖−sin〗⁡𝛼&cos⁡𝛼 )] = [■8(1&[email protected]&1)] [■8(cos⁡〖𝛼+cos⁡𝛼 〗&〖−sin〗⁡〖𝛼+sin⁡𝛼 〗@sin⁡𝛼 〖−sin〗⁡𝛼&cos⁡〖𝛼+cos⁡𝛼 〗 )]= [■8(1&[email protected]&1)] [■8(2cos⁡𝛼&[email protected]&2cos⁡𝛼 )]= [■8(1&[email protected]&1)] Since the matrices are equal, corresponding elements are equal 2cos 𝛼 = 1 cos⁡𝛼 = 1/2 cos⁡𝛼 = cos⁡〖60°〗 Comparing angles 𝛼 = 60° 𝛼 = 60° × 𝜋/(180°) 𝛼 = 𝜋/3 So the correct answer is (B) (As 𝑐𝑜𝑠⁡〖60°〗= 1/2)

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.