> with(linalg):
> K[red]:=matrix(4,4,[[56,-18,-18,-32],[-18,176,-32,-96],[-18,-32,176,-9
> 6],[-32,-96,-96,512]]);

                           [ 56    -18    -18    -32]
                           [                        ]
                           [-18    176    -32    -96]
                 K[red] := [                        ]
                           [-18    -32    176    -96]
                           [                        ]
                           [-32    -96    -96    512]

> f:=a^2*vector([5,20,20,80]);

                             2
                       f := a  [5, 20, 20, 80]

> Phi:=linsolve(K[red],f);

                        [    2      2      2       2]
                        [23 a   71 a   71 a   227 a ]
                 Phi := [-----, -----, -----, ------]
                        [ 39     156    156    624  ]

> Phi:=map(evalf,%);

         [              2                2                2
  Phi := [0.5897435897 a , 0.4551282051 a , 0.4551282051 a ,

                      2]
        0.3637820513 a ]

> 
