A matrix $P$ is decomposed into its symmetric part $S$ and skew symmetric part $V$. If $$S= \begin{pmatrix} -4 & 4 & 2 \\ 4 & 3 & 7/2 \\ 2 & 7/2 & 2 \end{pmatrix}, \: \: V= \begin{pmatrix} 0 & -2 & 3 \\ 2 & 0 & 7/2 \\ -3 & -7/2 & 0 \end{pmatrix}$$

then matrix $P$ is

1. $\begin{pmatrix} -4 & 6 & -1 \\ 2 & 3 & 0 \\ 5 & 7 & 2 \end{pmatrix} \\$
2. $\begin{pmatrix} -4 & 2 & 5 \\ 6 & 3 & 7 \\ -1 & 0 & 2 \end{pmatrix} \\$
3. $\begin{pmatrix} 4 & -6 & 1 \\ -2 & -3 & 0 \\ -5 & -7 & -2 \end{pmatrix} \\$
4. $\begin{pmatrix} -2 & 9/2 & -1 \\ -1 & 81/4 & 11 \\ -2 & 45/2 & 73/4 \end{pmatrix}$

We know that any square matrix  $M$  can be expressed as sum of symmetric and skew-symmetric matrices,

i.e.    $M=\frac{1}{2}(M+M^{T})+\frac{1}{2}(M-M^{T})$,   where the first and the second term on the RHS indicate the symmetric and skew-symmetric matrices respectively.

So, for the given question, option B turns out to be the only one satisfying the above equation.

Correct Option: B

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