Why does Gaussian elimination for band matrices take $\omega$ operations to eliminate the first element?

Question

I am currently reading through G. Strang’s “Linear Algebra and its applications” and there is this chapter about band and symmetric matrices which just does not stop confusing me. In this case we have a band matrix with the band width $\omega$ and the textbook tells me, that in order to eliminate one element below the leading one during the first step of elimination we require $\omega$ operations, but I cannot see how that’s possible, because for the elimination of that element we have to conduct 1 division of the first row by the leading element, which takes $\omega$ operations, and $\omega$ multiplications-subtractions, which adds up to 2$\omega$ operations. For those of you, who want to check for more details, it is nearly the end if the chapter 1.6 that this info is presented.