# contrast matrix for multiple comparisons in the model

In the following model I want to create a contrast matrix (K) corresponding to the global null hypothesis that all interaction terms present in the model are zero and test both the global hypothesis and all hypotheses corresponding to each of the interaction terms. Can model matrix be used as a contrast matrix in this case?

library(HSAUR)
data(clouds)
attach(clouds)
clouds_formula <- rainfall ~ seeding + seeding:(sne + cloudcover + prewetness + echomotion) + time
clouds_lm <- lm(clouds_formula, data = clouds)
summary(clouds_lm)

K <- model.matrix(clouds_formula, data = clouds) # contrast matrix
summary(glht(clouds_lm, linfct=K))