Example 22 - Express matrix B as sum of symmetric and skew - Symmetric and skew symmetric matrices

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
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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)] 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)] 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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