%%%%%%%%%%%%%%%%%%%%%
%%  Example 3.1, p. 24 of notes
%%%%%%%%%%%%%%%%%%%%

A=[1 1.82 3.3124 2.03;1 2.29 5.2441 3.28;1 4.88 23.8144 3.73]

A =

    1.0000    1.8200    3.3124    2.0300
    1.0000    2.2900    5.2441    3.2800
    1.0000    4.8800   23.8144    3.7300

rref(A)

ans =

    1.0000         0         0   -6.1962
         0    1.0000         0    5.9984
         0         0    1.0000   -0.8124

%%%%%%%%%%%%%%%%
%%  Quadratic interpolant to (-1,2) (1,1), (3,3).
%%%%%%%%%%%%%%

A=[1 -1 1 2;1 1 1 1;1 3 9 3]

A =

     1    -1     1     2
     1     1     1     1
     1     3     9     3

rref(A)

ans =

    1.0000         0         0    1.1250
         0    1.0000         0   -0.5000
         0         0    1.0000    0.3750

format rat
ans

ans =

       1              0              0              9/8     
       0              1              0             -1/2     
       0              0              1              3/8     

%%%%%%%%%%%%%%%%
%%  quadratic interpolant of (0,1) (2,4) (2,5)
%%%%%%%%%%%%%%%

A=[1 0 0 1; 1 2 4 4;1 2 4 5]

A =

       1              0              0              1       
       1              2              4              4       
       1              2              4              5       

rref(A)

ans =

       1              0              0              0       
       0              1              2              0       
       0              0              0              1       

%%  Example 3.3 p. 27

A=[1 30 900 27000 313.8;1 40 1600 64000 55.4;1 50 2500 125000 92.6;1 60 3600 216000 149.6]

A =

       1             30            900          27000           1569/5     
       1             40           1600          64000            277/5     
       1             50           2500         125000            463/5     
       1             60           3600         216000            748/5     

rref(A)

ans =

       1              0              0              0          28103/5     
       0              1              0              0         -23138/67    
       0              0              1              0           3497/500   
       0              0              0              1           -102/2219  

format short
ans

ans =

   1.0e+03 *

    0.0010         0         0         0    5.6206
         0    0.0010         0         0   -0.3453
         0         0    0.0010         0    0.0070
         0         0         0    0.0010   -0.0000

format long
ans

ans =

   1.0e+03 *

  Columns 1 through 3

   0.001000000000000                   0                   0
                   0   0.001000000000000                   0
                   0                   0   0.001000000000000
                   0                   0                   0

  Columns 4 through 5

                   0   5.620600000000000
                   0  -0.345343333333333
                   0   0.006994000000000
   0.001000000000000  -0.000045966666667

quiy
{??? Undefined function or variable 'quiy'.
} 
quit