How to find $B$ by solving the following linear system: $s_k$ $B$ ${s_k}^T$ $=1,$

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How to find $B$ by solving the following linear system:

$s_k$ $B$ ${s_k}^T$ $=1,$ $\qquad$ for $k=1 ... ,p$.

Where $s_k$ is a $1\times3$ row_vector from the matrix

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

and p $\ge$ 6

This system is supposed to find the 6 entries of a $3\times3$ symmetric matrix.

I would like to use Matlab to find this solution.

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Where is the problem ? If $p=6$, then one has a linear system of $6$ equations in the $6$ unknowns $b_{i,j}$, $i\leq j$. Write explicitly these equations. In general, the determinant of this system is non-zero and there is a unique solution.