Number of arithmetic operations

Nov 2009
ive been attempting to get this in my brain for a long time (Angry) read books, searched the net etc ..and this is my last resort!

can anyone explain (briefly if you want!) why/how:

For Gaussian elimination: At the kth step, we have:

n - k divisions (multipliers)
(n - k)^2 subtractions and multiplications (matrix update)
(n - k) subtractions and multiplications (updating vector b)

how do you get n - k or (n - k)^2
i know you must count the operations, but how?? it looks random