question_answer 1)

 Express the following matrices as the sum of a symmetric and a skew symmetric matrix :       (i)              (ii)       (iii)   (iv)  

Answer:

(i) Let       and       Let                                is a symmetric matrix.       Also, let                                     .        is a skey symmetric matrix.       Now             Thus A is represented as the sum a symmetric and a skey symmetric matrix. (ii)    Let             Let                                      is a symmetric matrix.       Also, let                          is a skew symmetric matrix.       Now             Thus A is represented as the sum of a symmetric and a skew symmetric matrix. (iii) Let       and       Let                                is a symmetry matrix.       Also, let                                      is a skew symmetric matrix.       Now P + Q =                   Thus A is represented as the sum of a symmetric and a skew symmetric matrix. (iii)   Let       and        Let                           is a symmetric matrix.       Also, let                                                  is a skew symmetric matrix.       Now             Thus A is represented as a sum of symmetric and a skew symmetric matrix.