Harj. 2 tehtävät 4 ja 5
=======================

> with(linalg):

#Teht. 4
=========

> A:=matrix(3,3,[1,1,-1,2,0,.5,0,2,.5]);

                                     [ 1  1  -1 ]
                                     [          ]
                                A := [ 2  0  .5 ]
                                     [          ]
                                     [ 0  2  .5 ]
--------------------------------------------------------------------------------
> b:=vector([0,8,16]);

                                b := [ 0, 8, 16 ]
--------------------------------------------------------------------------------
> Ab:=augment(A,b);

                                   [ 1  1  -1   0 ]
                                   [              ]
                             Ab := [ 2  0  .5   8 ]
                                   [              ]
                                   [ 0  2  .5  16 ]
----------------------------------------------------------------------------
> backsub(gausselim(Ab));

                [ 2.000000000, 6.000000000, 8. ]
----------------------------------------------------------------------------
> linsolve(A,b);

                    [ 2.000000000, 6.000000000, 8.000000000 ]

## Eli I1=2, I2=6, I3=8  (Ampeeria)

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> #Teht. 4
> 
> A:=matrix([[1,0,0,1],[0,0,1,1],[0,1,1,0],[1,1,0,0]]);

                                    [ 1  0  0  1 ]
                                    [            ]
                                    [ 0  0  1  1 ]
                               A := [            ]
                                    [ 0  1  1  0 ]
                                    [            ]
                                    [ 1  1  0  0 ]
--------------------------------------------------------------------------------
> b:=vector([1000,1600,2200,1600]);

                         b := [ 1000, 1600, 2200, 1600 ]
--------------------------------------------------------------------------------
> linsolve(A,b);

             [ - _t[1] + 1000, _t[1] + 600, - _t[1] + 1600, _t[1] ]
--------------------------------------------------------------------------------
>## Eli x1=1000-t
        x2=600+t
        x3=1600-t
        x4=t

Jotta kaikki > 0, oltava: 0 < t < 1000     (eli 0< x4 < 1000 )

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restart;