The only solution is that both the coefficient matrix and the augmented matrix are full, rA = rB = 3;; There is no solution to set the coefficient matrix smaller than the expansion matrix ra.
The coefficient matrix here is
a 1 1
1 a 1
1
The extension matrix is
a 1 1 a-3
1 a 1 -2
1 1 a -2
Don't tell me you don't want it.