Date: Aug 15, 2013 8:18 PM
Author: Barry Gallegos
Subject: How many (0,1)-matrices F satisfy E≤F?

If E=
[1 0 1 1]
[0 0 0 1] How many (0,1)-matrices F satisfy E<=F?
[1 0 0 0] How many (0,1)-matrices G satisfy G<=E?

I am not sure exactly how to define this personally, other than to say that my Text seems to point to this:
Let E=(e_ij)_(m×n),F=(e_ij )_(m×n),be two m × n (0,1)-matrices. We say that E precedes, or is less than,F,and we write E <= F,if e_ij<=f_ij,for all
1 <= i <= m,1 <= j <= n.

So what I think is that I have to matrices which are E&G.
If I state that there are 5 zeros and 7 ones. this means that E?F= 2^7 because there are 2 matrices and in this instance the zeros are greater than the ones which means 2^7. Opposite is true for G?E which becomes 2^5.

If I am understanding this correctly. I am hoping someone on this forum can help me out with this understanding.