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From: "printer newbie!" <newsboost@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Matrix inversion problem - What's going on?
Date: Tue, 12 Apr 2011 03:58:01 -0700 (PDT)
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On 11 Apr., 18:41, "Florin Neacsu" <fneac...@gmail.com> wrote:
> "printer newbie!" <newsbo...@gmail.com> wrote in message <82709a89-8b9f-41ca-90b4-c9738d23a...@d11g2000yqo.googlegroups.com>...
> > Dear all
>
> > I've uploaded this pdf-file:
> >http://www.2shared.com/document/o9q5B5Rw/Matlab_matrix_inversion.html
>
> > As you can see, I'm using Matlab:
>
> > 1) with two different matrices: A=[1 2; 3 4;5 6] and A=[1 2; 3 4;5 5]
> > and b=[1;2;3], meaning that:
> > 2) x=A\b can easily be found
> > 3) A*x = b, right? NO! Not in the second case!
>
> > Any hints/explanations are most welcome. I've put some comments in the
> > uploaded pdf-file and I guess that those of you who'll answer knows
> > everything about illposed problems, SVD and possible some other things
> > that I don't know of. I also tried to find the conditioning number for
> > the two matrices, however I'm a bit lost and can't come up with a good
> > explanation myself.
>
> As it was said above, this is an overdetermined system. If you are looking for an unique solution, then you system must have one of its lines equal to a linear combination of the two others.
> In general if you have p equations and n unknowns (with p>n for overdetermined), your system must have n linear independent equations, hence p-n linear dependent eq.

Ok, thanks. So the number of rows is the number of equations and the
number of columns is the number of unknowns...

So it was just a coincidence that it worked out for the first matrix,
but not the second...

What property (of the matrix A) is it then, that makes it work out
great for the first A-matrix, when they're both the same physical size
(3x2)? Are any lines in the first matrix linear combinations of
another line?