Is a Mlogit error caused by a variable column that contains only 0's?

I'm analysing data using mlogit. For a certain data.frames logit1 and logit2, this works perfectly fine.

However, if I create a certain subset data.frame logit3 and conduct mlogit in the exact same way, it gives the following error:

"Error in solve.default(H, g[!fixed]) : 
  Lapack routine dgesv: system is exactly singular: U[3,3] = 0"

This is how my code looks like:

mylogit3 <- mlogit.data(logit3, shape="long", alt.var="alt", id.var="ID", choice="choice", sep=",")

mnl3 <- mlogit(choice ~ -1 + con +X11+X12+X21+X22+X31+X32+X41+X42+X51+X61+X62, data=mylogit3)

The only difference between logit1 and logit3 is that column X12 only contains 0's. Is this causing the problem, and how can I work around the error?