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

Last updated at Aug. 16, 2021 by Teachoo

Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. Since your board exams are coming, why not help Teachoo create more videos and content by supporting us? Please click on this link to make a donation

Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. Since your board exams are coming, why not help Teachoo create more videos and content by supporting us? Please click on this link to make a donation

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