Ex 3.3, 10 (ii) - Express the matrix as sum of symmetric and - Teachoo - Ex 3.3

part 2 - Ex 3.3, 10 (ii) - Ex 3.3 - Serial order wise - Chapter 3 Class 12 Matrices
part 3 - Ex 3.3, 10 (ii) - Ex 3.3 - Serial order wise - Chapter 3 Class 12 Matrices

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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)] Let, P = 𝟏/𝟐 (A + A’) = [■8(6&−2&2@−2&3&−1@2&−1&3)] P’ = [■8(6&−2&2@−2&3&−1@2&−1&3)] = P Since P = P’ P is a symmetric matrix. Let, Q = 𝟏/𝟐 (A − A’) = [■8(0&0&0@0&0&0@0&0&0)] Q’ = [■8(0&0&0@0&0&0@0&0&0)] = −[■8(0&0&0@0&0&0@0&0&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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo