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Ex 3.3, 10 - Chapter 3 Class 12 Matrices - Part 10

Ex 3.3, 10 - Chapter 3 Class 12 Matrices - Part 11

 

 

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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&−[email protected]&2)] 1/2 (A + A’) = 1/2 ([■8(1&5@−1&2)]" + " [■8(1&−[email protected]&2)]) = 1/2 [■8(2&[email protected]&4)] = [■8(1&[email protected]&2)] 1/2 (A – A’) = 1/2 ([■8(1&5@−1&2)]−[■8(1&−[email protected]&2)]) = 1/2 [■8(0&6@−6&0)] = [■8(0&3@−3&0)] Let, P = 𝟏/𝟐 (A + A’) = [■8(1&[email protected]&2)] P’ = [■8(1&[email protected]&2)] = P Since P = P’ P is a symmetric matrix. Let, Q = 𝟏/𝟐 (A − A’) = [■8(0&3@−3&0)] Q’ = [■8(0&−[email protected]&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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.