Confounding and rank of expanded design matrix

#1
Hello,

If I have confounding with 1 defining equation two columns of the expanded design matrix are equal (blocks and the confounding factor). When there are two defining equations there are two columns confounded with blocks and blocks are determined using two L functions.

What is the relationship between the two effects that are confounded and blocks? It appears that the expanded design matrix is not of full rank which means that X'X has a 0 determinant.

I have a 2^4 factorial in 4 blocks of 4. I=ABD=BCD=AC.

Sincerely,
Mary A. Marion