I calculate determinant of a 6x6 matrix with smath and Excel, but the results are different. Whats the problem?

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Question1.sm (3.83 KiB) downloaded 1292 time(s).

SMath gives -5.6406E-7
MS Excel/LibreOffice gives -1.7486E-7

If you use some online solvers, they give you other different results:
http://matrix.reshish.com gives -3.497202527569246e-7
http://www.bluebit.gr/matrix-calculator gives 0.000000437150316

...and so on...

Finally, WolframAlpha gives zero.

It is floating-point error side-effect, so this result should not be considered "erroneous"; when doing floating-point math you always should be prepared to such things. See relevant Wikipedia article, and especially this brilliant series: http://randomascii.wordpress.com/category/floating-point/

Maxima gives the exact answer.

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detmaxima.sm (6.51 KiB) downloaded 1215 time(s).