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Ex 3.3
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) You are here
Ex 3.3, 10 (iii) Important
Ex 3.3, 10 (iv)
Ex 3.3, 11 (MCQ) Important
Ex 3.3, 12 (MCQ)
Last updated at March 22, 2023 by Teachoo
Ex 3.3, 10 Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (ii) [■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)] Let A = [■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)] A’ = [■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)] 1/2 (A + A’) = 1/2 ([■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)]" + " [■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)]) = 1/2 [■8(12&−4&[email protected]−4&6&−[email protected]&−2&6)] = [■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)] 1/2 (A − A’) = 1/2 ([■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)]−[■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)]) = 1/2 [■8(0&0&[email protected]&0&[email protected]&0&0)] = [■8(0&0&[email protected]&0&[email protected]&0&0)] Let, P = 𝟏/𝟐 (A + A’) = [■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)] P’ = [■8(6&−2&[email protected]−2&3&−[email protected]&−1&3)] = P Since P = P’ P is a symmetric matrix. Let, Q = 𝟏/𝟐 (A − A’) = [■8(0&0&[email protected]&0&[email protected]&0&0)] Q’ = [■8(0&0&[email protected]&0&[email protected]&0&0)] = −[■8(0&0&[email protected]&0&[email protected]&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