Solving linear algebraic eqns. in vector (matrix) notation ?

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
(%i3) load(eigen);
(%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.

Any comments are appreciated.
Regards,Radovan