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) You are here
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)
Last updated at April 16, 2024 by Teachoo
Ex 3.3, 6 If (i) A = [■8(cos𝛼&sin𝛼@−sin𝛼&cos𝛼 )] , then verify that A’A = I Solving L.H.S. A’A Given A = [■8(cos𝛼&sin𝛼@−sin𝛼&cos𝛼 )] So, A’ = [■8(𝐜𝐨𝐬𝜶&−𝐬𝐢𝐧𝜶@𝐬𝐢𝐧𝜶&𝐜𝐨𝐬𝜶 )] A’ A = [■8(cos𝛼&〖−sin〗𝛼@sin𝛼&cos𝛼 )] [■8(cos𝛼&sin𝛼@−sin𝛼&cos𝛼 )] = [■8(cos𝛼.cos𝛼+〖(−sin〗〖𝛼)〖(−sin〗〖𝛼)〗 〗&cos𝛼 〖.sin〗𝛼+〖(−sin〗〖𝛼)cos𝛼 〗@sin𝛼. cos𝛼+cos〖𝛼 〖(−sin〗〖𝛼)〗 〗&sin𝛼.sin𝛼+cos〖𝛼 .cos𝛼 〗 )] = [■8(cos2𝛼+sin2𝛼&sin〖𝛼 cos〖𝛼−sin〖𝛼 cos𝛼 〗 〗 〗@sin𝛼 cos〖𝛼−sin𝛼 〗 cos𝛼&sin2𝛼+cos2 a)] = [■8(𝐜𝐨𝐬𝟐𝜶+𝐬𝐢𝐧𝟐 𝜶&𝟎@𝟎&𝐬𝐢𝐧𝟐𝜶+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