In the edgeR vignette, they mention additive models when dealing with paired samples. So if this was our design:

data.frame(Subject = rep(c(1,2,3), each = 2), Treatment = rep(c("C","F"), 3))
  Subject Treatment

1       1         C
2       1         T
3       2         C
4       2         T
5       3         C
6       3         T

And if we wanted to look at the effects of treatment, while adjusting for the subject, the model matrix would look like this:

  model.matrix(~Subject + Treatment)

Does this also apply for when we want to adjust for another variable? Let's say we have treatment (not paired) and gender as such:

  Samples   Treatment   Gender
Sample_1    Control     M
Sample_2    Control     M
Sample_3    Control     M
Sample_4    Treatment   M
Sample_5    Treatment   M
Sample_6    Treatment   M
Sample_7    Control     F
Sample_8    Control     F
Sample_9    Control     F
Sample_10   Treatment   F
Sample_11   Treatment   F
Sample_12   Treatment   F

Would a model matrix like this using the additive model adjust for gender?

model.matrix(~Gender + Treatment)