Problem

The Hilbert matrix of order n is defined by ai j = (i + j − 1)−1 for 1?i, j ?n. It is of...

The Hilbert matrix of order n is defined by ai j = (i + j − 1)1 for 1?i, j ?n. It is often used for test purposes because of its ill conditioned nature. Define

for x using procedures Gauss and Solve, and see whether the result is as predicted. Do the case n = 2 by hand to see what difficulties occur in the computer.

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