### Is there an easy way to get the matrix of coefficients from a product of a matrix and a vector?

I have a matrix multiplication of the form

$$ B = A x $$

or

$$
\begin{pmatrix} a_{11} x_1 + a_{12} x_2 + a_{13} x_3 \\ a_{21} x_1 + a_{22} x_2 + a_{23} x_3 \\ a_{31} x_1 + a_{32} x_2 + a_{33} x_3 \end{pmatrix} = \begin{pmatrix}
a_{11} & a_{12} & a_{13}\\
a_{21} & a_{22} & a_{23}\\
a_{31} & a_{32} & a_{33}
\end{pmatrix}
\cdot
\begin{pmatrix}
x_1 \\
x_2 \\
x_3
\end{pmatrix}
$$

Is there a way in Sage to factor $B$ in a way where I give it $x$ and it returns $A$?

Edited from a question posted by someone else at the Mathematica Stackexchange