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Ex 3.3, 6 If (i) A = [■8(cos⁡𝛼&sin⁡𝛼@−sin⁡𝛼&cos⁡𝛼 )] , then verify that A’A = I Solving L.H.S. A’A Given A = [■8(cos⁡𝛼&sin⁡𝛼@−sin⁡𝛼&cos⁡𝛼 )] So, A’ = [■8(𝐜𝐨𝐬⁡𝜶&−𝐬𝐢𝐧⁡𝜶@𝐬𝐢𝐧⁡𝜶&𝐜𝐨𝐬⁡𝜶 )] A’ A = [■8(cos⁡𝛼&〖−sin〗⁡𝛼@sin⁡𝛼&cos⁡𝛼 )] [■8(cos⁡𝛼&sin⁡𝛼@−sin⁡𝛼&cos⁡𝛼 )] = [■8(cos⁡𝛼.cos⁡𝛼+〖(−sin〗⁡〖𝛼)〖(−sin〗⁡〖𝛼)〗 〗&cos⁡𝛼 〖.sin〗⁡𝛼+〖(−sin〗⁡〖𝛼)cos⁡𝛼 〗@sin⁡𝛼. cos⁡𝛼+cos⁡〖𝛼 〖(−sin〗⁡〖𝛼)〗 〗&sin⁡𝛼.sin⁡𝛼+cos⁡〖𝛼 .cos⁡𝛼 〗 )] = [■8(cos2⁡𝛼+sin2𝛼&sin⁡〖𝛼 cos⁡〖𝛼−sin⁡〖𝛼 cos⁡𝛼 〗 〗 〗@sin⁡𝛼 cos⁡〖𝛼−sin⁡𝛼 〗 cos𝛼&sin2⁡𝛼+cos2 a)] = [■8(𝐜𝐨𝐬𝟐⁡𝜶+𝐬𝐢𝐧𝟐 𝜶&𝟎@𝟎&𝐬𝐢𝐧𝟐⁡𝜶+𝐜𝐨𝐬𝟐 𝒂)] Using sin2 θ + cos2 θ = 1 = [■8(1&0@0&1)] = I = R.H.S Hence L.H.S = R.H.S Hence Proved

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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.