Question

Find and , when

Answer 1

(i)

Given, matrix A is,

A=[ 0 a b −a 0 c −b −c 0 ]

Then the transpose of A becomes,

A ′ =[ 0 −a −b a 0 −c b c 0 ]

Substitute the values of A and A ′ in A+ A ′ ,

A+ A ′ =[ 0 a b −a 0 c −b −c 0 ]+[ 0 −a −b a 0 −c b c 0 ] =[ 0 0 0 0 0 0 0 0 0 ] 1 2 ( A+ A ′ )=[ 0 0 0 0 0 0 0 0 0 ]

Thus, the value of 1 2 ( A+ A ′ )=[ 0 0 0 0 0 0 0 0 0 ].

Substitute the values of A and A ′ in A− A ′ ,

A− A ′ =[ 0 a b −a 0 c −b −c 0 ]−[ 0 −a −b a 0 −c b c 0 ] =[ 0 2a 2b −2a 0 2c −2b −2c 0 ] 1 2 ( A− A ′ )=[ 0 a b −a 0 c −b −c 0 ]

Thus, the value of 1 2 ( A- A ′ ) is [ 0 a b −a 0 c −b −c o ].