> with(linalg):
Warning, the protected names norm and trace have been redefined and
unprotected

> B:=matrix(4,4,[[4*R, -3*R,0,0], [-3*R,5*R,0,0], [0, 0, 9*R, -4*R],    
>   [0,0,-4*R,10*R]]); 

                      [4 R     -3 R     0       0  ]
                      [                            ]
                      [-3 R    5 R      0       0  ]
                 B := [                            ]
                      [ 0       0      9 R     -4 R]
                      [                            ]
                      [ 0       0      -4 R    10 R]

> b:=matrix(1,4,[5*V,-10*V,-5*V,10*V]);

                 b := [5 V    -10 V    -5 V    10 V]

> y:=matrix(1,4,[I[a], I[b], I[c], I[d]]);

                 y := [I[a]    I[b]    I[c]    I[d]]

> y:=transpose(linsolve(B,transpose(b)));

                   [  5 V       25 V      5 V     35 V]
              y := [- ----    - ----    - ----    ----]
                   [  11 R      11 R      37 R    37 R]

# Alternativ bietet Maple folgende Version an:
> solve({4*R*I[a] - 3*R*I[b] = 5*V,                                     
>                           -3*R*I[a] + 5*R*I[b]  = -10*V,
>  9*R*I[c] - 4*R*I[d]  = -5*V,
> -4*R*I[c] + 10*R*I[d] = 10*V},
> {I[a], I[b], I[c], I[d]});

                5 V            25 V           5 V          35 V
      {I[a] = - ----, I[b] = - ----, I[c] = - ----, I[d] = ----}
                11 R           11 R           37 R         37 R

> 
> 
# Ergnzung: Man ndere die Bezeichungen gem Ic -> Ia, Ia ->Ib, Ib
# ->Ic, Id
# 
> solve({4*R*I[b] - 3*R*I[c] = 5*V,                                     
>                           -3*R*I[b] + 5*R*I[c]  = -10*V,
>  9*R*I[a] - 4*R*I[d]  = -5*V,
> -4*R*I[a] + 10*R*I[d] = 10*V},
> {I[a], I[b], I[c], I[d]});

              35 V           5 V            5 V            25 V
      {I[d] = ----, I[a] = - ----, I[b] = - ----, I[c] = - ----}
              37 R           37 R           11 R           11 R

> 
