I want to perform linear regression, but some elements of the regressor variable are already known. How do I tell cvx that it must solve for the other variables and predefine the known elements?

Example:
Y = A*X

where Y is (for instance) a 3x10 matrix, A is 3x3 and X is 3x10.

Yes that would work! But what if my variables are changing between replications (e.g. A(1,1)=x(1))? Or what if my A matrix is large? Is there a way to automate this?