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Last updated at Aug. 16, 2021 by Teachoo

Transcript

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)] Let, P = 𝟏/𝟐 (A + A’) = [■8(1&2@2&2)] P’ = [■8(1&2@2&2)] = P Since P = P’ P is a symmetric matrix. Let, Q = 𝟏/𝟐 (A − A’) = [■8(0&3@−3&0)] Q’ = [■8(0&−3@3&0)] = – [■8(0&3@−3&0)] = −Q Since Q = − Q’ Q is a skew symmetric matrix. 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

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

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) You are here

Ex 3.3, 11 (MCQ) Important

Ex 3.3, 12 (MCQ)

Chapter 3 Class 12 Matrices (Term 1)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.