[R] why NA coefficients

[array chip]

Hi, I am trying to run ANOVA with an interaction term on 2 factors (treat has 7 levels, group has 2 levels). I found the coefficient for the last interaction term is always 0, see attached dataset and the code below:

> test<-read.table("test.txt",sep='\t',header=T,row.names=NULL)
> lm(y~factor(treat)*factor(group),test)

Call:
lm(formula = y ~ factor(treat) * factor(group), data = test)

Coefficients:
                  (Intercept)                 factor(treat)2                 factor(treat)3  
                     0.429244                       0.499982                       0.352971  
               factor(treat)4                 factor(treat)5                 factor(treat)6  
                    -0.204752                       0.142042                       0.044155  
               factor(treat)7                 factor(group)2  factor(treat)2:factor(group)2  
                    -0.007775                      -0.337907                      -0.208734  
factor(treat)3:factor(group)2  factor(treat)4:factor(group)2  factor(treat)5:factor(group)2  
                    -0.195138                       0.800029                       0.227514  
factor(treat)6:factor(group)2  factor(treat)7:factor(group)2  
                     0.331548                             NA 


I guess this is due to model matrix being singular or collinearity among the matrix columns? But I can't figure out how the matrix is singular in this case? Can someone show me why this is the case?

Thanks

John
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