Unexpected result calculating the determinant of a singular matrix (42S)

[Valentin Albillo]

(10-24-2019 06:34 AM)Werner Wrote:  

(10-23-2019 11:06 PM)Valentin Albillo Wrote:  I can't try and find a counterexample to what you state because I don't have an HP48-whatever to check if my attempts work or not so I'll take your word for it.

Suppose you calculate the determinants using Cramer's rule. The intermediate products would then be no larger than 100^7 = 1e14, the final result being 1 - so you'll lose at most 14 digits. I think ;-)

Not necessarily. For a 7x7 matrix with 2-digit integer elements each individual intermediate product would be no longer than 7x2 = 14 digits, that's correct, but to compute the determinant you're adding up many such products and thus the result can wildly exceed 14 digits, so if you're using just 15 digits for the intermediate terms and final result you're likely to lose them all and then some.

Regards and have a nice weekend.
V.