# Ex 3.3, 6 (ii) - Chapter 3 Class 12 Matrices

Last updated at April 16, 2024 by Teachoo

Ex 3.3

Ex 3.3, 1

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 You are here

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)

Chapter 3 Class 12 Matrices

Serial order wise

Last updated at April 16, 2024 by Teachoo

Ex 3.3, 6 (ii) If A = [■8(sin𝛼&cos𝛼@−cos𝛼&sin𝛼 )] , then verify that A’ A = I Solving L.H.S A’ A Given A = [■8(sin𝛼&cos𝛼@−cos𝛼&sin𝛼 )] So, A’ = [■8(sin𝛼&〖−cos〗𝛼@cos𝛼&sin𝛼 )] A’ A = [■8(sin𝛼&〖−cos〗𝛼@cos𝛼&sin𝛼 )] [■8(sin𝛼&cos𝛼@〖−cos〗𝛼&sin𝛼 )] = [■8(sin𝛼 〖.sin〗𝛼+〖(−cos〗〖𝛼)〖(−cos〗〖𝛼)〗 〗&sin𝛼 〖.cos〗𝛼+〖(−cos〗〖𝛼)〖(sin〗〖𝛼)〗 〗@cos𝛼 〖.sin〗𝛼+sin〖𝛼 〖(−cos〗〖𝛼)〗 〗&cos𝛼 〖.cos〗𝛼+sin〖𝛼 〖.sin〗𝛼 〗 )] = [■8(sin2𝛼+cos2𝛼&sin〖𝛼 cos〖𝛼−cos〖𝛼 sin𝛼 〗 〗 〗@cos𝛼 sin〖𝛼−sin𝛼 〗 cos𝛼&cos2𝛼+sin2𝛼)] = [■8(𝐬𝐢𝐧𝟐𝜶+𝐜𝐨𝐬𝟐𝜶&𝟎@𝟎&𝐜𝐨𝐬𝟐𝜶+𝐬𝐢𝐧𝟐𝜶)] Using sin2 θ + cos2 θ = 1 = [■8(1&0@0&1)] = I = R.H.S Hence L.H.S = R.H.S Hence Proved