# Example 22 - Chapter 3 Class 12 Matrices

Last updated at Jan. 17, 2020 by Teachoo

Last updated at Jan. 17, 2020 by Teachoo

Transcript

Example 22 Express the matrix B = [■8(2&−2&−4@−1&3&4@1&−2&−3)] as the sum of a symmetric and a skew symmetric matrix. B = [■8(2&−2&−4@−1&3&4@1&−2&−3)] B’ = [■8(2&−1&1@−2&3&−2@−4&4&−3)] Finding 1/2 (B + B’) and 1/2 (B − B’) 1/2 (B + B’) = 1/2 ([■8(2&−2&−4@−1&3&4@1&−2&−3)]+[■8(2&−1&1@−2&3&−2@−4&4&−3)]) = 1/2 [■8(4&−3&−3@−3&6&2@−3&2&−6)] = [■8(2&(−3)/2&(−3)/2@(−3)/2&3&1@(−3)/2&1&−3)] 1/2 (B – B’) = 1/2 ([■8(2&−2&−4@−1&3&4@1&−2&−3)]−[■8(2&−1&1@−2&3&−2@−4&4&−3)]) = 1/2 [■8(0&−1&−5@1&0&6@5&−6&0)] = [■8(0&(−1)/2&(−5)/2@1/2&0&3@5/2&−3&0)] Let, P = 𝟏/𝟐 (B + B’) = [■8(2&(−3)/2&(−3)/2@(−3)/2&3&1@(−3)/2&1&−3)] P’ = [■8(2&(−3)/2&(−3)/2@(−3)/2&3&1@(−3)/2&1&−3)] = P Since P’ = P P is a symmetric matrix. Let, Q = 𝟏/𝟐 (B − B’) = [■8(0&(−1)/2&(−5)/2@1/2&0&3@5/2&−3&0)] Q’ = [■8(0&1/2&5/2@(−1)/2&0&−3@(−5)/2&3&0)] = – [■8(0&(−1)/2&(−5)/2@1/2&0&3@5/2&−3&0)] Since Q’ = − Q Q is a skew symmetric matrix. Now, P + Q = 1/2 (B + B’) + 1/2 (B − B’) = B Thus, B is a sum of symmetric & skew symmetric matrix

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Example 22 Important You are here

Example 23 Deleted for CBSE Board 2021 Exams only

Example 24 Important Deleted for CBSE Board 2021 Exams only

Example 25 Important Deleted for CBSE Board 2021 Exams only

Example 26 Important

Example 27 Important

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.