Re: 4x4 matrices using Cramer's Rule


Han de Bruijn wrote:
Virgil wrote:


snip


Is there any particular reason why you need to use Cramer's rule?

There are much better methods.

Cramer's rule is only useful for very small matrices, BUT there are MANY
problems with such small matrices. Cramer's rule has the advantage that
it gives always an easy solution iff the matrix is non-singular. Integer
problems as the above can also be programmed in such a way that floating
point operations are avoided altogether, preserving an "exact" solution,
as you have demonstrated. An obvious drawback is that Cramer's rule very
quickly runs out of performance. Therefore use is delimited to matrices
with rank < 6 or 7 or some such. Quite a severe limitation, admittedly.

Han de Bruijn

rank 6 or 7? I think doing numeric examples with anything more than 4
with CR is not advisable.

OTOH, Cramer's rule is a great theoretical tool because it's gives
formulas for the solution. Other methods like Gaussian elimination are
"algorithms." It's tough to do proofs and such by using
variables/symbols with algorithms.

.

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