"also the figure I get comes out to be emtpy"
You need to use array operations, not matrix operations:
>> [X,Y] = meshgrid(2:10,2:10);
>> U = X./(X.^2+Y.^2);
>> V = Y./(X.^2+Y.^2);
Tip: if you are not doing linear algebra then most likely you should be using array operations:
"I don't understand. What does this mean??"
The matrix operation mrdivide you used by mistake is trying to solve an unsolvable set of equations. The fact that it solves sets of equations is explained in its documentation, which is why you should read the documentation for every operator that you use, no matter how trivial you think it is.