Last updated at May 29, 2018 by Teachoo

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Ex 3.3, 10 Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (i) [■8(3&5@1&−1)] Let A = [■8(3&5@1&−1)] A’ = [■8(3&1@5&−1)] 1/2 (A + A’) = 1/2 ([■8(3&5@1&−1)]+ [■8(3&1@5&−1)]) = 1/2 [■8(6&6@6&−2)] = [■8(3&3@3&−1)] 1/2 (A – A’) = 1/2 ([■8(3&5@1&−1)]" − " [■8(3&1@5&−1)]) = 1/2 [■8(0&4@−4&0)] = [■8(0&2@−2&0)] Now, P + Q = 1/2 (A + A’) + 1/2 (A − A’) = A Thus, A is a sum of symmetric & skew symmetric matrix Ex 3.3, 10 Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (ii) [■8(6&−2&2@−2&3&−1@2&−1&3)] Let A = [■8(6&−2&2@−2&3&−1@2&−1&3)] A’ = [■8(6&−2&2@−2&3&−1@2&−1&3)] 1/2 (A + A’) = 1/2 ([■8(6&−2&2@−2&3&−1@2&−1&3)]" + " [■8(6&−2&2@−2&3&−1@2&−1&3)]) = 1/2 [■8(12&−4&4@−4&6&−2@4&−2&6)] = [■8(6&−2&2@−2&3&−1@2&−1&3)] 1/2 (A − A’) = 1/2 ([■8(6&−2&2@−2&3&−1@2&−1&3)]−[■8(6&−2&2@−2&3&−1@2&−1&3)]) = 1/2 [■8(0&0&0@0&0&0@0&0&0)] = [■8(0&0&0@0&0&0@0&0&0)] Now, P + Q = 1/2 (A + A’) + 1/2 (A − A’) = A Thus, A is a sum of symmetric & skew symmetric matrix Ex 3.3, 10 Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (iii) [■8(3&3&−1@−2&−2&1@−4&−5&2)] Let A = [■8(3&3&−1@−2&−2&1@−4&−5&2)] A’ = [■8(3&−2&−4@3&−2&−5@−1&1&2)] 1/2 (A + A’) = 1/2 ([■8(3&3&−1@−2&−2&1@−4&−5&2)]" + " [■8(3&−2&−4@3&−2&−5@−1&1&2)]) = 1/2 [■8(6&1&−5@1&−4&−4@−5&−4&4)] = [■8(3&1/2&−5/2@1/2&−2&−2@−5/2&−2&2)] 1/2 (A − A’) = 1/2 ([■8(3&3&−1@−2&−2&1@−4&−5&2)]" − " [■8(3&−2&−4@3&−2&−5@−1&1&2)]) = 1/2 [■8(0&5&3@−5&0&6@−3&−6&0)] = [■8(0&−5/2&−3/2@5/2&0&−3@3/2&3&0)] Now, P + Q = 1/2 (A + A’) + 1/2 (A − A’) = A Thus, A is a sum of symmetric & skew symmetric matrix Ex 3.3, 10 Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (iv) [■8(1&5@−1&2)] Let A = [■8(1&5@−1&2)] A’ = [■8(1&−1@5&2)] 1/2 (A + A’) = 1/2 ([■8(1&5@−1&2)]" + " [■8(1&−1@5&2)]) = 1/2 [■8(2&4@4&4)] = [■8(1&2@2&2)] 1/2 (A – A’) = 1/2 ([■8(1&5@−1&2)]−[■8(1&−1@5&2)]) = 1/2 [■8(0&6@−6&0)] = [■8(0&3@−3&0)] Now, P + Q = 1/2 (A + A’) + 1/2 (A − A’) = A Thus, A is a sum of symmetric & skew symmetric matrix

Chapter 3 Class 12 Matrices

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 You are here

Ex 3.3, 12 Important

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.