> with(linalg):
> K[red]:=matrix(4,4,[[4,-1,-2,-1],[-1,8,-2,-2],[-2,-2,16,-2],[-1,-2,-2,
> 8]]);

                             [ 4    -1    -2    -1]
                             [                    ]
                             [-1     8    -2    -2]
                   K[red] := [                    ]
                             [-2    -2    16    -2]
                             [                    ]
                             [-1    -2    -2     8]

> f:=(3/4)*a^2*vector([1,2,4,2]);

                                 2
                       f := 3/4 a  [1, 2, 4, 2]

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

                        [    2      2      2      2]
                        [87 a   27 a   27 a   27 a ]
                 Phi := [-----, -----, -----, -----]
                        [ 140    56     70     56  ]

> Phi:=map(evalf,%);

         [              2                2                2
  Phi := [0.6214285714 a , 0.4821428571 a , 0.3857142857 a ,

                      2]
        0.4821428571 a ]

> 
