Ex 3.2, 6 - Chapter 3 Class 12 Matrices

Transcript

Ex 3.2, 6 Simplify cos θ[■8(cos θ&sin θ@−sin θ&cos θ)] + sin θ [■8(sin θ&−cos θ@cos θ&sin θ)] cos θ[■8(cos θ&sin θ@−sin θ&cos θ)] + sin θ [■8(sin θ&−cos θ@cos θ&sin θ)] = [■8("cos " θ("cos " θ)&cos θ(sin θ)@cos θ (−𝑠𝑖𝑛θ)&cos θ(cos θ))] + [■8(sin θ(sin θ)&sin θ(−"cos " θ) @sin θ("cos " θ)&sin θ(sin θ))] = [■8(𝐜𝐨𝐬𝟐 𝜽&𝐜𝐨𝐬 𝛉 𝐬𝐢𝐧 𝜽@−𝐜𝐨𝐬 𝛉 𝐬𝐢𝐧 𝜽&𝐜𝐨𝐬𝟐 𝜽)] + [■8(𝐬𝐢𝐧𝟐 𝜽&−𝐜𝐨𝐬 𝛉 𝐬𝐢𝐧 𝜽@𝐬𝐢𝐧 𝛉 𝐜𝐨𝐬 𝜽&𝐬𝐢𝐧𝟐 𝜽)] = [■8(cos2 θ+sin2 θ&sin θ cos θ−cos θ sin θ@−cos θ sin θ+sin θ cos θ&cos2 θ+sin2 θ)] = [■8(cos2 θ+sin2 θ&0@0&cos2 θ+sin2 θ)] = [■8(𝟏&𝟎@𝟎&𝟏)]