Determinant equation and its tautological solution.

(*Mathematica 8 start*)nn = 7;
a = RandomReal[{-1, 1}]
Print["b = the numbers fed in"]
b = Table[n + RandomReal[{-1, 1}], {n, 1, nn}]
A = Table[
   Table[If[n == k, a, If[n > k, RandomReal[{-1, 1}], 0]], {k, 1,
     nn}], {n, 1, nn}];
B = Transpose[A]*b[[Range[nn]]];
c = (x /. Solve[Expand[Det[A.B - x*A]] == 0, x])/a;
Print["c = solutions to the polynomial"]
Sort[c, Less]
Print["The matrix A.B"]
TableForm[A.B]
(*end*)