How can I decompose a matrix into my favorite form?

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Nima Nikmehr 2020-6-9

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Dear All,

I have a matrix called M, which includes some variables like x. I want to describe matrix M(x) in another form like A+BXC, in which A, B, and C should be matrices with constant numbers and variables (x) should be defined as a column matrix X.

As an example, M is a 3 by 3 matrix and only includes a variable x. A should be a matrix 3 by 3, B should be 3 by 1, and C 1 by 3. So, X is a 1 by 1 matrix.

M=[-12x 5 2;

6 -4 3x;

3x 4 -10];

Now. how can I define matrix M in the form of A+BXC in MATLAB? (what will be the elements of A, B, C)