I have a dataset like so

df <- data.frame(condition=rep(c("c","l"),each=12),family=rep(c(20,21,27,30),each=3))
df
   condition family
1          c     20
2          c     20
3          c     20
4          c     21
5          c     21
6          c     21
7          c     27
8          c     27
9          c     27
10         c     30
11         c     30
12         c     30
13         l     20
14         l     20
15         l     20
16         l     21
17         l     21
18         l     21
19         l     27
20         l     27
21         l     27
22         l     30
23         l     30
24         l     30

I would like to compare condition c and l within families. I created a model like so:

design.mat <- model.matrix(~condition+family,df)

creating this model matrix

   (Intercept) conditionl family20 family21 family27 family30
1            1          0        1        0        0        0
2            1          0        1        0        0        0
3            1          0        1        0        0        0
4            1          0        0        1        0        0
5            1          0        0        1        0        0
6            1          0        0        1        0        0
7            1          0        0        0        1        0
8            1          0        0        0        1        0
9            1          0        0        0        1        0
10           1          0        0        0        0        1
11           1          0        0        0        0        1
12           1          0        0        0        0        1
13           1          1        1        0        0        0
14           1          1        1        0        0        0
15           1          1        1        0        0        0
16           1          1        0        1        0        0
17           1          1        0        1        0        0
18           1          1        0        1        0        0
19           1          1        0        0        1        0
20           1          1        0        0        1        0
21           1          1        0        0        1        0
22           1          1        0        0        0        1
23           1          1        0        0        0        1
24           1          1        0        0        0        1
attr(,"assign")
[1] 0 1 2 2 2 2
attr(,"contrasts")
attr(,"contrasts")$condition
[1] "contr.treatment"

attr(,"contrasts")$family
[1] "contr.treatment"

I then ran

eb <- DGEList(counts)
ebg <- estimateGLMCommonDisp(eb,design.mat)

but I get this error:

Error in glmFit.default(y, design = design, dispersion = dispersion, offset = offset,  : 
  Design matrix not of full rank.  The following coefficients not estimable:
 family30

I also tried

design.mat <- model.matrix(~0+condition+family,df)

as suggested in another post, but it still does not work. Any ideas on how this can be tackled is highly appreciated. Thanks.