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Question -

Express the followingmatrices as the sum of a symmetric and a skew symmetric matrix:



Answer -

(i) 

(ii) 

(iii) 

(iv) 


Solution

(i)

Thus,  is a symmetric matrix.

Thus,  is a skew-symmetricmatrix.

Representing A asthe sum of P and Q:

(ii)

Thus,  is a symmetric matrix.

Thus, is a skew-symmetricmatrix.

Representing A asthe sum of P and Q:

(iii)

Thus, is a symmetric matrix.

Thus,  is a skew-symmetricmatrix..

Representing A asthe sum of P and Q:

(iv)

Thus,  is a symmetric matrix.

Thus,is a skew-symmetric matrix.

Representing A asthe sum of P and Q:

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