# Ex 3.3, 12

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 3.3, 12 If A = [■8(cos 𝛼&〖−sin〗𝛼@sin𝛼&cos𝛼 )] , then A + A’ = I , if the value of α is A. 𝛑/𝟔 B. 𝛑/𝟑 C. π D. 𝟑𝛑/𝟐 A = [■8(cos𝛼&〖−sin〗𝛼@sin𝛼&cos𝛼 )] A’= [■8(cos𝛼&sin𝛼@〖−sin〗𝛼&cos𝛼 )] and I = [■8(1&0@0&1)] Given A + A’ = I [■8(cos𝛼&〖−sin〗𝛼@sin𝛼&cos𝛼 )] + [■8(cos𝛼&sin𝛼@〖−sin〗𝛼&cos𝛼 )] = [■8(1&0@0&1)] [■8(cos〖𝛼+cos𝛼 〗&〖−sin〗〖𝛼+sin𝛼 〗@sin𝛼 〖−sin〗𝛼&cos〖𝛼+cos𝛼 〗 )]= [■8(1&0@0&1)] [■8(2cos𝛼&0@0&2cos𝛼 )]= [■8(1&0@0&1)] Since the matrices are equal, corresponding elements are equal 2cos 𝛼 = 1 cos𝛼 = 1/2 cos𝛼 = cos〖60°〗 Comparing angles 𝛼 = 60° 𝛼 = 60° × 𝜋/(180°) 𝛼 = 𝜋/3 So the correct answer is (B)

Ex 3.1, 7
Important

Ex 3.1, 9 Important

Example 18 Important

Example 19 Important

Ex 3.2, 7 Important

Ex 3.2, 12 Important

Ex 3.2, 16 Important

Ex 3.2, 17 Important

Ex 3.2, 20 Important

Example 22 Important

Ex 3.3, 4 Important

Ex 3.3, 10 Important

Ex 3.3, 12 Important You are here

Ex 3.4, 15 Important

Ex 3.4, 17 Important

Example 28 Important

Misc. 3 Important

Misc. 9 Important

Misc. 11 Important

Misc. 13 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.