


Examples
Example 2
Example 3 Important
Example 4
Example 5 Important
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11 Important
Example 12
Example 13 Important
Example 14
Example 15
Example 16 Important
Example 17
Example 18 Important
Example 19
Example 20 Important
Example 21
Example 22 Important You are here
Example 23 Deleted for CBSE Board 2022 Exams
Example 24 Important Deleted for CBSE Board 2022 Exams
Example 25 Important Deleted for CBSE Board 2022 Exams
Example 26 Important
Example 27 Important
Example 28
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