An Example: Determinant of a Hilbert Matrix

Consider the problem of computing the determinant of a 10 by 10 Hilbert
matrix. The (i,j)-th entry of a Hilbert matrix is given by 1/(i+j+1).
First do the computation using rational numbers to obtain the exact result.
The result given by hardware floats is correct only to four significant digits
of precision. In the jargon of numerical analysis, the Hilbert matrix is said
to be "ill-conditioned".
Now repeat the computation at a higher precision using Float.
Reset digits to its default value.