# How to factor a matrix by a list of symbolic variables

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Fernando am 21 Okt. 2014
Kommentiert: Aleja Campo am 5 Dez. 2020
My problem is the following:
I have a 3x1 matrix of symbolic equations (let's call it Y) that I want to divide into two matrixes that we will call Phi and Theta. Phi will be a 3xn wide matrix, and Theta will be a nx1 column matrix. I have a list of variables that will be in the nx1 matrix, the rest will be in the Phi matrix, where Y = Phi*Theta.
Is there a way to factorize and build the matrixes programatically with the Symbolic Math Toolbox?
Thanks!
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Aleja Campo am 5 Dez. 2020
Hi
Yes I had the same problem, you can use the equationsToMatrix function
Best

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### Akzeptierte Antwort

Bruno Pop-Stefanov am 22 Okt. 2014
Are the equations in Y linear in the variables in Theta? If yes, this is a simple linear system of equations, which you can solve symbolically with the linsolve function. Take a look at Solve a System of Linear Equations for an example.
If they are algebraic equations, you can try to use the solve function. Take a look at the example in Solve a System of Algebraic Equations.
In addition, you can have an overview of the equation-solving tools that Symbolic Math Toolbox provides in the documentation at:
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