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# How to solve a system of matrix equations?

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Christoph Müßig on 18 Dec 2018
Commented: Matt J on 18 Dec 2018
Given are two lists of 87 3x1 vectors each. I also know that when multiplying a 3x3 matrix by the nth vector of the first list, I get the nth vector of the second list. The 3x3 matrix is ​​the same in all these calculations. So it's a system of equations with 87 equations and I want to solve for the content of the 3x3 matrix. I've tried to approximate the solution with Machine Learning and Curve Fitting, but there are too few equations for that. How could I solve this problem mathematically or approximate the solution with Matlab?
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Torsten on 18 Dec 2018
And the rotation axis in your case passes through the origin ?

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### Accepted Answer

Matt J on 18 Dec 2018
For example, given
A=rand(3,87);
X=rand(3,3);
B=X*A;
you can reconstruct X by doing,
X=B/A;
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Matt J on 18 Dec 2018
You're welcome, but please Accept-click the answer, if that's the case.

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