Re: again on matsolve()

[Bill Allombert <allomber@math.u-bordeaux.fr>]

On Sun, Dec 11, 2005 at 06:06:19PM +0100, Alessio Rocchi wrote:
> Hi everybody.
> I'm stille experiencing problems while using matsolve().
> 
> I run the following command:
> matsolve([1,1,0,0,0;2,2,0,0,0;3,3,0,0,0;1,0,0,2,0;2,0,2,0,0;0,1,1,0,1;4,0,0,0,1;2,0,1,1,0;1,0,0,0,0;2,1,0,0,0;3,2,0,0,0;2,0,0,2,0],[6,36,216,98,100,165,176,140,2,12,72,196]~)
> First matrix is [12x5] and the second [12x1].
> All I can get is always -->*** matsolve: inconsistent data in gauss.<--
> May anybody explain me the reason for this to happen?

Yes, a [12x5] matrix cannot be invertible:
? ??matsolve
matsolve(x,y):

   x being an invertible matrix and y a column vector,  finds the
   solution u of
   x*u = y, using Gaussian elimination.  This has the same effect as,
   but is a bit
   faster, than x^{-1}*y.

You probably want to use matinverseimage() instead:

? ??matinverseimage
matinverseimage(M,y):

   gives  a column vector belonging to the inverse image z of the column vector
or  matrix  y by the matrix M if one exists  (i.e such that Mz = y),  the empty
vector otherwise.  To get the complete inverse image, it suffices to add to the
result any element of the kernel of x obtained for example by matker.

Cheers,
Bill.