0 votes

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

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

0 votes

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**