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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=Ax

or

(a11x1+a12x2+a13x3a21x1+a22x2+a23x3a31x1+a32x2+a33x3)=(a11a12a13a21a22a23a31a32a33)(x1x2x3)

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