Question

Express the matrix $\left[\begin{array}{ccc}1& -2& 3\\ 3& 4& 5\\ 5& 7& 9\end{array}\right]$ as the sum of a symmetric and a skew-symmetric matrix.

Answer 1

$A=[1-23345579]$

$A^1=[135-247359]$

$\frac{1}{2}[A+A^1]=[11/241/246469]$

$\frac{1}{2}[A-A^1]=[0-5/2-15/20-1110]$

$[1-23345579]=[11/241/246469]+[0-5/2-15/20-1110]$