Re: Why is Maple able to give me RREF without encountering "divide by zero"?

On Apr 23, 8:51 pm, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On 22 Apr 2007 14:03:04 -0700, "dillog...@xxxxxxxxx"



<dillog...@xxxxxxxxx> wrote:
On Apr 22, 6:59 pm, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On 21 Apr 2007 20:19:16 -0700, "dillog...@xxxxxxxxx"

<dillog...@xxxxxxxxx> wrote:
hi

Why is Maple able to give me RREF without encountering "divide by
zero"?
This makes no sense.

Find a book on linear algebra!

_Any_ matrix has a RREF. Finding it _never_ involves division
by zero.

The matrix is clearly singular.
A:=Matrix([[0,0,0,0,0,0,1,1,1],[4,2,1,4,2,1,4,2,1],
[196,28,4,98,14,2,49,7,1],[19600,980,49,2800,140,7,400,20,1],
[1488400,24400,400,74420,1220,20,3721,61,1],
[123254404,677222,3721,2020564,11102,61,33124,182,1],
[9910998916,18118828,33124,54456038,99554,182,299209,547,1],
[804752526400,490702760,299209,1471211200,897080,547,2689600,1640,1],
[65132001793600,13235521600,2689600,39714635240,8070440,1640,24216241,4921,1]]);
b:=Vector([2,7, 20, 61, 182, 547, 1640, 4921, 14762]);
ReducedRowEchelonForm(<A|b>);
MatrixInverse(A);
Error, (in LinearAlgebra:-LA_Main:-MatrixInverse) singular matrix

I should ask my college for money back.

I doubt it. If you can show me a book that says a singular
matrix does not have a RREF I'll be amazed - the fact that
you got some wrong ideas in your head somehow is not your
college's fault.

If RREF can do the job without ever encountering "divide by zero", why
were we taught gaussian elimination and did programming assignment on
that?
Can you give justification for not teaching a more generic model
first?
All students in our class were required to purchase a TI-82
calculator, and did gaussian elimination programming on that. Are you
going to vouch for the curriculum quality for all the schools?

You're very confused about something, it's hard to say exactly
what. Neither RREF nor gaussian elimination involves division
by zero. A correct program for either one never does division
by zero. So I really can't figure out the right response
to your questions about why this and why that...

I've got that misunderstanding "wrapped up", sorta speak.
I don't really care what cause it, it's behind me now.
I admit you can do RREF without division:
I've got a demostration here:
http://www.cap-lore.com/MathPhys/Field/RREF.html

I don't want to touch or think about gaussian elimination right now.
The way I had to deal with it was whenever there is "division by
zero", return "singular". That was probably wrong.




************************

David C. Ullrich

************************

David C. Ullrich


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