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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