# [Maxima] Solving linear algebraic eqns. in vector (matrix) notation ?

Sun Dec 30 00:53:00 CST 2007

```Dear all!

I am trying to solve some simple linear algebraic system of equations
using array, vector, matrix notation.
Here is my first attempt:

(%i1) n1:makelist(n1[k],k,1,6);
(%o1)                 [n1 , n1 , n1 , n1 , n1 , n1 ]
1    2    3    4    5    6
(%i2) n2:makelist(n2[k],k,1,6);
(%o2)                 [n2 , n2 , n2 , n2 , n2 , n2 ]
1    2    3    4    5    6
(%o3)  D:/PROGRA~1/MAXIMA~1.0/share/maxima/5.12.0/share/matrix/eigen.mac
(%i4) n1:columnvector(n1);
[ n1  ]
[   1 ]
[     ]
[ n1  ]
[   2 ]
[     ]
[ n1  ]
[   3 ]
(%o4)               [     ]
[ n1  ]
[   4 ]
[     ]
[ n1  ]
[   5 ]
[     ]
[ n1  ]
[   6 ]
(%i5) n2:columnvector(n2);
[ n2  ]
[   1 ]
[     ]
[ n2  ]
[   2 ]
[     ]
[ n2  ]
[   3 ]
(%o5)               [     ]
[ n2  ]
[   4 ]
[     ]
[ n2  ]
[   5 ]
[     ]
[ n2  ]
[   6 ]
(%i6) S: matrix([-1,0],[1,-1],[0,1],[1,0],[-1/2,-1/2],[0,0]);
[ - 1  0 ]
[        ]
[  1 - 1 ]
[        ]
[  0   1 ]
[        ]
(%o6)            [  1  0  ]
[        ]
[  1   1 ]
[- - - - ]
[  2   2 ]
[        ]
[  0   0 ]
(%i7) eps:columnvector(makelist(eps[k],k,1,2));
[ eps  ]
[    1 ]
(%o7)              [      ]
[ eps  ]
[    2 ]
(%i8) m: n1-n2+S.eps;
[  - n2  + n1  - eps        ]
[      1     1      1       ]
[                           ]
[ - n2  + n1  - eps  + eps  ]
[     2     2      2      1 ]
[                           ]
[    - n2  + n1  + eps      ]
[        3     3      2     ]
[                           ]
(%o8)        [    - n2  + n1  + eps      ]
[        4     4      1     ]
[                           ]
[              eps    eps   ]
[                 2       1 ]
[ - n2  + n1  - ---- - ---- ]
[     5     5     2     2   ]
[                 ]
[       n1  - n2            ]
[         6     6           ]

So far so good!. I was trying to figure out how to solve the column
vector m (every element equals to 0) ie. 6 linear equations in 6
variables. What should I do in order to find, say, vector n2[k],k,1,6 (I
know how to assign values to other variables - if needed)?. On the other
hand, I suppose there must be some other, more elegant way to work with
and solve equations with indexed variables. I might missing something
but could not find in Maxima book or help any examples of this kind.

```