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

"dillogimp@xxxxxxxxx" <dillogimp@xxxxxxxxx> writes:

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?

Gaussian elimination is somewhat faster than Gauss-Jordan elimination
(which corresponds to RREF), and better at preserving band structure.
Neither should encounter "divide by zero". If you encounter a zero
in what would be a pivot position, you exchange that row with one
below that has a nonzero entry in that column, or go on to the next
column if there are none of those.

Can you give justification for not teaching a more generic model
first?

Who says it's more generic?

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?

I wouldn't dream of it. My guess is that for this particular assignment,
your instructor allowed programs that would attempt to divide by 0 when
the matrix was singular, not realizing that you would think this was
a general feature of Gaussian elimination. Or it could be that this
particular instructor made a mistake - that does happen sometimes. But
your textbook, if you had one, would be less likely to make this mistake.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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