Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 3.3, 10 (iv) - Chapter 3 Class 12 Matrices
Last updated at May 29, 2023 by Teachoo
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
Serial order wise
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&−[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
