Express a matrix $A$ as the sum of a symmetric and a skew symmetric matrix I'm trying to express 
$$A = \left[ \begin{array} { r r r } { 2 } & { - 2 } & { - 4 } \\ { - 1 } & { 3 } & { 4 } \\ { 1 } & { - 2 } & { - 3 } \end{array} \right]$$
as the sum of a symmetric and a skew symmetric matrix.
So far I have tried this:
converting into transpose
$A ^ { \prime } = \left[ \begin{array} { c c c } { 2 } & { - 1 } & { 1 } \\ { - 2 } & { 3 } & { 4 } \\ { - 4 } & { 4 } & { - 3 } \end{array} \right]$
well this dont seem to be symmteric matrix according to me. are there steps to be taken. 
and for skew symmteric matrix i tried to do like this 
transpose of equation 
$A ^ { \prime } = \left[ \begin{array} { c c c } { 2 } & { - 1 } & { 1 } \\ { - 2 } & { 3 } & { 4 } \\ { - 4 } & { 4 } & { - 3 } \end{array} \right]$
took minus as common 
$A ^ { \prime } = \left[ \begin{array} { c c c } { - 2 } & { 1 } & { - 1 } \\ { 2 } & { - 3 } & { 2 } \\ { 4 } & { - 4 } & { 3 } \end{array} \right]$
can you guide me how to proceed with them

HINT
Recall that for any square matrix $A$
$$A=\frac{A+A^T}{2}+\frac{A-A^T}{2}$$
and
$$\left(\frac{A+A^T}{2}\right)^T=\frac{A^T+A}{2}=\frac{A+A^T}{2}$$
$$\left(\frac{A-A^T}{2}\right)^T=\frac{A^T-A}{2}=-\frac{A-A^T}{2}$$
