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Chapter 3 Class 12 Matrices
Ex 3.1, 9 (MCQ) Important
Example 18 Important
Example 19
Ex 3.2, 7 (i)
Ex 3.2, 12 Important
Ex 3.2, 16 Important
Ex 3.2, 17 Important
Ex 3.2, 20 Important
Example 22 Important
Ex 3.3, 4 Important
Ex 3.3, 10 (i) Important You are here
Ex 3.3, 12 (MCQ)
Question 15 Important Deleted for CBSE Board 2024 Exams
Question 17 Important Deleted for CBSE Board 2024 Exams
Example 25
Question 3 Important Deleted for CBSE Board 2024 Exams
Misc 6 Important
Misc 8 Important
Misc 9 (MCQ)
Chapter 3 Class 12 Matrices
Last updated at June 8, 2023 by Teachoo
Ex 3.3, 10 Express the following matrices as the sum of a symmetric and a skew symmetric matrix: (i) [■8(3&5@1&−1)] Let A = [■8(3&5@1&−1)] A’ = [■8(3&1@5&−1)] 𝟏/𝟐 (A + A’) = 1/2 ([■8(3&5@1&−1)]+ [■8(3&1@5&−1)]) = 1/2 [■8(6&6@6&−2)] = [■8(𝟑&𝟑@𝟑&−𝟏)] 𝟏/𝟐 (A – A’) = 1/2 ([■8(3&5@1&−1)]" − " [■8(3&1@5&−1)]) = 1/2 [■8(0&4@−4&0)] = [■8(𝟎&𝟐@−𝟐&𝟎)] Let, P = 𝟏/𝟐 (A + A’) = [■8(3&3@3&−1)] P’ = [■8(3&3@3&−1)] = P Since P‘ = P P is a symmetric matrix. Let, Q = 𝟏/𝟐 (A − A’) = [■8(0&2@−2&0)] Q’ = [■8(0&−2@2&0)] = – [■8(0&2@−2&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