Shelley, to find a non-trivial solution you have to find the null space of your data matrix.
You data matrix with a column of ones (for the intercept term E):
>> M = [[1,1,1,1; 2,3,2,2; 4,5,4,6; 0,1,3,4],[1;1;1;1]]
M =
1 1 1 1 1
2 3 2 2 1
4 5 4 6 1
0 1 3 4 1
Regress will give you the trivial solution that is zeros. Since M above is rank deficient there are a family of solutions. The non-trivial solution would be the null space which you can compute as follows:
>> null(M)
ans =
-0.3536
0.3536
-0.7071
0.3536
0.3536
