Express A as the sum of a symmetric and a skew-symmetric matrix, where `A=[(3,5),(-1,2)]`

Explanation

`A =[(3,5),(-1,2)],"then" A' =[(3,-1),(-1,2)]`
`Let" " p=(1)/(2)(A+A')=(1)/(2)[(6,4),(4,4)]=[(3,2),(2,2)]=p'`
`Thus" " p=(1)/(2)(A+A')` is a symmetric matrix.
Also, let `Q" =(1)/(2)(A+A')=(1)/(2)[(0,6),(-6,0)]=[(0,3),(-3,0)]`
Then,` Q[(0,-3),(3,0)]=[(0,3),(-3,0)]=Q`
thus, `Q = (1)/(2)(A-A')` is a skew-symmetric matrix.
Now, `P+Q= [(3,2),(2,2)]+[(0,3),(-3,0)]=[(3,5),(-1,2)]=A`
Hence, A is represented as the sum of a symmetric and a skew-symmetric matrix.