sage: L = [[2,4,16],[1/2,1,2],[1,1,1]]
sage: A = matrix(RDF, L)
sage: xvalues = [sqrt(2), 2, 4]

sage: L2 = [[i^2 for i in xvalues], [log(i, 2) for i in xvalues], [1 for i 
in xvalues]]
sage: A2 = matrix(RDF, L2)
sage: print (A - A2).norm()
1.11022302463e-16

sage: b = vector(RDF, [5, 20, 106])
sage: print A.solve_right(b)
(153.25, -37.875, -9.375)
sage: print A.inverse() * b
(153.25, -37.875, -9.375)

sage: print A2.solve_right(b)
(128.0, -32.0, -9.375)
sage: print A2.inverse() * b
(153.25, -37.875, -9.375)

The third output is quite off and I don't think it can be attributed to 
numerical error. Any idea what is happening?

Rado

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