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# If $A=\begin{bmatrix}6&8&5\\4&2&3\\9&7&1\end{bmatrix}$ is the sum of symmetric matrix $B$ and skew-symmetric matrix $C$ then $B$ is

$\begin{array}{1 1}(a)\;\begin{bmatrix}6&6&7\\6&2&5\\7&5&1\end{bmatrix}&(b)\;\begin{bmatrix}0&2&-2\\-2&5&-2\\2&2&0\end{bmatrix}\\(c)\;\begin{bmatrix}6&6&7\\-6&2&-5\\-7&5&1\end{bmatrix}&(d)\;\begin{bmatrix}0&6&-2\\2&0&-2\\-2&-2&0\end{bmatrix}\end{array}$

We have $A=\begin{bmatrix}6&8&5\\4&2&3\\9&7&1\end{bmatrix}$
Symmetric matrix B=$\large\frac{A+A'}{2}$
$\Rightarrow B=\large\frac{1}{2}$$\bigg[\begin{bmatrix}6&8&5\\4&2&3\\9&7&1\end{bmatrix}+\begin{bmatrix}6&4&9\\8&2&7\\5&3&1\end{bmatrix}\bigg]$
$\Rightarrow \begin{bmatrix}6&6&7\\6&2&5\\7&5&1\end{bmatrix}$
Hence (a) is the correct answer.