Solve linear system [tex]s_kB{s_k}^T[/tex] [tex]=1,[/tex]

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How to find [tex]B[/tex] by solving the following linear system:

[tex]s_k[/tex] [tex]B[/tex] [tex]{s_k}^T[/tex] [tex]=1,[/tex] [tex]\qquad[/tex] for [tex]k=1 ... ,p[/tex] .


Where [tex]s_k[/tex] is a [tex]1\times3[/tex] row_vector from the matrix

[tex]S= [s_1 ... s_p]^T= \begin{pmatrix}
{s_1}_x & {s_1}_y & {s_1}_z \\
\vdots & \vdots& \vdots \\
{s_p}_x & {s_p}_y & {s_p}_z \\
\end{pmatrix}[/tex]

and p [tex]\ge[/tex] 6

This system is supposed to find the 6 entries of a [tex]3\times3[/tex] symmetric matrix.
I would like to use Matlab to find this solution.