Von: Hans Georg Feichtinger [hans.feichtinger@univie.ac.at]
Gesendet: Dienstag, 29. Jnner 2008 17:50

TestRecommend.pdf solutions

1) A = rand(3),  % will give you an invertible matrix

   rref(A),   % will allow you to inspect if the matrix is OK

You can/should also try to set

  The equation desribed by  A*x = b is easily solved
  by  x1 = inv(A) * b; % but since we are not sure about
  the invertibility of A, better use  x2 = pinv(A) * b;
  control:  check = norm(x1 - x2),
Ab = [A,b] is of course the "extended system matrix of the inhomogeneous system", and  rref(Ab) presents the same result!

AAb = Ab;
AAb(4,:) =  rand(1,3)*AAb;  % fabricating a random linear
   % combination of the first three rows! hence making
   % a CONSISTENT system of equations is now a 4 x 3 system
   % and still has a solution
AA= AAb(:,1:3); bb = AAb(:,4);

either via  rref(AAb)  or  pinv(AA) *  bb !!
(note that here   inv(AA) could NEVER work!)

2) just set up the matrix  A = [4,5,1; 5,3,3; 0,1,5]; b = [11,9,5]
  and do what has been described above!

3) generate the points as in pluroots, you should get  360 points
   in the complex plane, call this sequence z  (they correspond to
   points in [0, 2*pi], if you want, so use perhaps
   bas = linspace(0, 2*pi,361) as a starting point (the first and last
   are then identified)
   then use polyval( coefficients, positions) to get it, and
   plot by some command like    plot(bas, real(polyval...));

OK?  Hope this helps


On Tue, January 29, 2008 17:19, XX wrote:
> If you could show me the codes for solving questions 1 and 2 (they are
> to do with linear equations), and also question 11 (to do with
> polynomials) I would be very grateful.
> Thanks!
>
> Quoting Hans Georg Feichtinger <hans.feichtinger@univie.ac.at>:
>
>> PS: No specific "solutions" planned. Do you have any specific
>> question in mind?
>>
>> Hgfei
>
