Using the ./ operator with the dot does element-wise division. Using / without the dot does matrix linear equation solving. So this operation:
x = a/b
is the solution to the following equation
x*b = a
I.e., conceptually you divide both sides of this equation on the right by b to get the solution above. This is simply a set of linear equations that MATLAB is solving using the "backslash" or "forwardslash" operator. E.g.,
>> a = [1 2;3 4;5 6]
a =
1 2
3 4
5 6
>> b = [3 4; 5 6;7 8]
b =
3 4
5 6
7 8
>> x = a/b
x =
1.5000 0 -0.5000
1.0000 0 0
0.5000 0 0.5000
>> x*b
ans =
1.0000 2.0000
3.0000 4.0000
5.0000 6.0000
