> The problem is rounding error. Over the rationals:
>
> sage: A = matrix(3, 3, [QQ(a) for a in [1, 0.106, 1.212, 3.8759765625,
> 0.04801171875, 3.972, 3.0625, 0.09325, 3.249]])
> sage: A
> [           1       53/500      303/250]
> [   3969/1024 12291/256000      993/250]
> [       49/16     373/4000    3249/1000]
>
> sage: A.rank()
>  2
>

Nice, seems like converting to rational would get around this rounding prob. 
   

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