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2020-07-03 08:21:16 -0600 received badge  Popular Question (source)
2019-02-09 20:02:25 -0600 commented question Is there an easy way to get the matrix of coefficients from a product of a matrix and a vector?

Ok, I should have used the word "rewrite" instead of "get" in my question.

2019-02-09 19:58:28 -0600 commented question Is there an easy way to get the matrix of coefficients from a product of a matrix and a vector?

Sorry, I wasn’t clear. I didn’t mean to ask to solve the equation in general. What I was wondering is if there is a simple function that just returns the matrix of coefficients ai,j in front of the xi’s. Just a purely formal exercise. In other words, just have the computer do the rewriting (splitting) B in the form of A x. Nothing else. Yes, I know, I could write a function myself, but maybe someone already did it. According to the answer on Stackexchange, it can be done easily in Mathematica.

2019-02-09 12:59:57 -0600 received badge  Student (source)
2019-02-08 17:11:11 -0600 asked a question 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