Newbie question solving lin sys

[John B. Thoo]

Hi.  I'm very new to using Octave.  I have two questions: 1. What am I 
doing wrong in the following?  2. How can I do it more elegantly?


I want to solve the system  Ax = T  where  A  is the  12x12  Vandermonde 
matrix

      [ 1  0  0   ...  0    ]
      [ 1  1  1   ...  1    ]
  A = [ 1  2  2^2 ...  2^11 ]
      [           ...       ]
      [ 1 11 11^2 ... 11^11 ]


  T = [ 22 28 31 39 46 53 56 55 49 42 33 27 ]'

To do this, I enter in Octave:

octave:51> A = fliplr(vander([0,1,2,3,4,5,6,7,8,9,10,11]));
octave:52> T = [22;28;31;39;46;53;56;55;49;42;33;27];
octave:53> A\T
ans =

    2.2000e+01
    1.2932e+02
   -3.3001e+02
    3.5674e+02
   -2.1174e+02
    7.7512e+01
   -1.8446e+01
    2.9092e+00
   -3.0191e-01
    1.9818e-02
   -7.4570e-04
    1.2250e-05

*But* when I go to check my answers, they seem to be off.  To check my 
answers, I enter in Octave:

octave:54> s = 0;
octave:55> 22 + 129.32*s - 330.01*s**2 + 356.74*s**3 - 211.74*s**4 + 
77.512*s**5 - 18.446*s**6 + 2.9092*s**7 - 0.30191*s**8 + 0.019818*s**9 - 
0.0007457*s**10 + 0.00001225*s**11
ans = 22
octave:56> s = 1;
octave:57> 22 + 129.32*s - 330.01*s**2 + 356.74*s**3 - 211.74*s**4 + 
77.512*s**5 - 18.446*s**6 + 2.9092*s**7 - 0.30191*s**8 + 0.019818*s**9 - 
0.0007457*s**10 + 0.00001225*s**11
ans = 28.002
octave:58> s = 3;

and so on.  The answers match well for the first few, but then they 
drift.  To summarize, I get

     s  |  answers from Octave  |  supposed to be (T)
   ---------------------------------------------------
     0  |        22             |        22
     1  |        28.002         |        28
     2  |        31.017         |        31
     3  |        38.996         |        39
     4  |        45.498         |        46
     5  |        50.205         |        53
     6  |        46.456         |        56
     7  |        30.029         |        55
     8  |       - 5.5781        |        49
     9  |       -62.227         |        42
    10  |      -145.80          |        33
    11  |      -245.29          |        27


TIA for your help.

---John.



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