For loop - Gaussian elimination

Hi guys and girls. Please could you assist me in understanding the for loop section in the following code (as a m file in the editor):

function x = Gauss(a,b)
ab = [a,b]
[R, C] = size(ab)
for j = 1:R-1
    for i = j + 1:R
        ab(i,j:C) = ab(i,j:C)-ab(i,j)/ab(j,j)*ab(j,j:C)
    end

the left side is the function ab for loops i.j:C (i think). It means that you can call up ab and it will look at inputs i,j:C? How does Matlab look at the right side? Sorry i am new to Matlab and struggling some late hours here...

[Geoff Hayes]

S - the left-side of the assignment

 ab(i,j:C)

means that columns j through C of row i will be updated with right-hand side of the assignment which is just

 ab(i,j:C)-ab(i,j)/ab(j,j)*ab(j,j:C)

Is this code that you have written or obtained from somewhere? While it has some of the steps from gaussian elimination it seems to be incomplete.