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Torsten

Posts: 1,182
Registered: 11/8/10

Re: Solve the system of equations
Posted: Feb 13, 2013 9:34 AM

Plain Text

"Milos Milenkovic" <m.milenkovic@mathworks.com> wrote in message <kfg5vq$8nk$1@newscl01ah.mathworks.com>...
> "Torsten" wrote in message <kfg06b$iqb$1@newscl01ah.mathworks.com>...
> > "Milos Milenkovic" <m.milenkovic@mathworks.com> wrote in message <kffujm$dk2$1@newscl01ah.mathworks.com>...
> > > Dear all,
> > > I have a system of equations D=A*X*B, X=?, A,B,D are known, but using the solve command, I obtain empty set as solution. The elements of matrices are:
> > >
> > > A=[0.06 0.07 0.08 0.09 0.1 0.09; 0.01 0.02 0.03 0.04 0.05 0.06; -0.01 -0.02 -0.03 -0.04 -0.04 0.05; 0 0.01 0.02 0.03 0.04 0.05; -0.06 -0.05 -0.04 -0.03 -0.02 -0.01;
> > > 0.01 0.02 0.03 0.04 0.05 0.06];
> > >
> > > syms X x11 x12 x13 x14 x15 x16 x21 x22 x23 x24 x25 x26 x31 x32 x33 x34 x35 x36 x41 x42 x43 x44 x45 x46 x51 x52 x53 x54 x55 x56 x61 x62 x63 x64 x65 x66;
> > >
> > > X=[x11 x12 x13 x14 x15 x16;x21 x22 x23 x24 x25 x26;x31 x32 x33 x34 x35 x36;x41 x42 x43 x44 x45 x46;x51 x52 x53 x54 x55 x56;x61 x62 x63 x64 x65 x66];
> > >
> > > B=[-1 0 0 0 0 0; 0 -1 0 0 0 0; 0 0 -1 0 0 0; 0 0 0 -1 0 0; 0 0 0 0 -1 0; 0 0 0 0 0 -1];
> > >
> > > D=[0.57 0.57 23.96 0 0.57 0.57; 0.57 0.57 23.96 0 0.57 0.57; 23.96 23.96 3027.70 0 23.96 23.96;0 0 0 0 0 0;0.57 0.57 23.96 0 0.57 0.57;0.57 0.57 23.96 0 0.57 0.57];
> > >
> > > What is the problem here?
> > >
> > > Best,
> > > Milos
> >
> > Why symbolic variables ?
> > X=-A\D .
> >
> > Best wishes
> > Torsten.
>
>
> Dear Torsten,
> thank you for your quick response!! Sorry, but I think that this solution is not good. The answer for X is:
> X =
> 1.0e+18 *
> 0.0329 0.0329 1.3812 0 0.0329 0.0329
> 0.0329 0.0329 1.3812 0 0.0329 0.0329
> -0.1643 -0.1643 -6.9060 0 -0.1643 -0.1643
> 0.0986 0.0986 4.1436 0 0.0986 0.0986
> -0.0000 -0.0000 -0.0000 0 -0.0000 -0.0000
> 0 0 0 0 0 0
> which, replaced in A*X*B is not equal to D =>
>
> A*X*B is
> Y=A*X*B
> Y =
> 1.0e+03 *
> 0.0013 0.0013 0.0040 0 -0.0027 -0.0027
> 0.0021 0.0021 0.0340 0 -0.0009 -0.0009
> 0.0212 0.0212 2.9232 0 0.0242 0.0242
> 0.0008 0.0008 0.0208 0 -0.0007 -0.0007
> -0.0027 -0.0027 -0.0904 0 -0.0007 -0.0007
> 0.0021 0.0021 0.0340 0 -0.0009 -0.0009
>
> but D is
> D =
> 1.0e+03 *
> 0.0006 0.0006 0.0240 0 0.0006 0.0006
> 0.0006 0.0006 0.0240 0 0.0006 0.0006
> 0.0240 0.0240 3.0277 0 0.0240 0.0240
> 0 0 0 0 0 0
> 0.0006 0.0006 0.0240 0 0.0006 0.0006
> 0.0006 0.0006 0.0240 0 0.0006 0.0006
>
> So the relation
> D=A*X*B is not fulfilled.
> Best,
> M

Your matrix A is singular (2nd and 6th row are identical) - so you can not expect that you can find X that satisfies your linear system exactly.
Take a look at the MATLAB documentation for the solution of underdetermined
linear systems of equations.

Best wishes
Torsten.