How to vectorice a set of linear system of equations over 4D and 3D matrices

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Dear
I have a 4D and a 3D matrix, and over them we have to perform the following operations:
for i=1 to n
for j=1 to m
v(i,j,:)=Jac(:,:,i,j)\F(:,i,j);
end
end
Is there any way to vectorize this operation in order to improve the efficiency?
Many thanks,

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