for the matrix `A=[{:(1,5),(6,7):}],` verify that :
(I) (A+A') is a symmetric matrix.
(ii) (A-A') is a skew symmetric matrix.

Answer

N/a

Explanation

`A=[{:(1,5),(6,7):}]`
`implies A'=[{:(1,5),(6,7):}]=[{:(1,6),(5,7):}]`
(i) `A+A'=[{:(1,5),(6,7):}]+[{:(1,6),(5,7):}]=[{:(2,11),(11,14):}]`
`implies (A+A')'=[{:(2,11),(11,14):}]=[{:(2,11),(11,14):}]=A+A'`
`implies ` A"A' is a symmetric matrix . Hence proved
`(ii) A-A'=[{:(1,5),(6,7):}]-[{:(1,6),(5,7):}]=[{:(0,-1),(1,0):}]`
`implies (A-A')' =[{:(0,-1),(1,0):}]=[{:(0,1),(-1,0):}]`
` =- [{:(0,-1),(0,1):}]=-(A-A')`
`implies ` is a skew symmetric matrix .
Hence proved .