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

> A:=matrix(4,3,[[-k[1],0,0],[k[1]+k[2]+k[3],-(k[2]+k[3]),0],[-(k[2]+k[3
> ]),k[2]+k[3]+k[4],-k[4]],[0,-k[4],k[4]]]);
> 

            [      -k[1]                   0               0  ]
            [                                                 ]
            [k[1] + k[2] + k[3]       -k[2] - k[3]         0  ]
       A := [                                                 ]
            [   -k[2] - k[3]       k[2] + k[3] + k[4]    -k[4]]
            [                                                 ]
            [        0                   -k[4]           k[4] ]

> a:=vector([-F,0,0,F]);
> 

                          a := [-F, 0, 0, F]

> G:=multiply(transpose(A),A);
> 

  G :=

        [    2                       2                 2
        [k[1]  + (k[1] + k[2] + k[3])  + (-k[2] - k[3])  ,

        (k[1] + k[2] + k[3]) (-k[2] - k[3]) + (-k[2] - k[3]) %1 ,

                            ]
        -(-k[2] - k[3]) k[4]]

        [
        [(k[1] + k[2] + k[3]) (-k[2] - k[3]) + (-k[2] - k[3]) %1 ,

                      2     2       2                  2]
        (-k[2] - k[3])  + %1  + k[4]  , -%1 k[4] - k[4] ]

        [                                      2         2]
        [-(-k[2] - k[3]) k[4] , -%1 k[4] - k[4]  , 2 k[4] ]

  %1 := k[2] + k[3] + k[4]

> g:=multiply(transpose(A),a);
> 

                    g := [k[1] F, -k[4] F, k[4] F]

> U:=linsolve(G,g): convert(U,matrix);
> 

        [ F  ]
        [----]
        [k[1]]

        [F (k[1] + k[2] + k[3])]
        [----------------------]
        [  (k[2] + k[3]) k[1]  ]

        [F

        (k[4] k[1] + k[2] k[4] + k[3] k[4] + k[1] k[2] + k[1] k[3])/(

        k[4] (k[2] + k[3]) k[1])]

> u[2]:=U[1];u[3]:=U[2];u[4]:=U[3];
> 

                                      F
                             u[2] := ----
                                     k[1]


                            F (k[1] + k[2] + k[3])
                    u[3] := ----------------------
                              (k[2] + k[3]) k[1]


  u[4] := F

        (k[4] k[1] + k[2] k[4] + k[3] k[4] + k[1] k[2] + k[1] k[3])/(

        k[4] (k[2] + k[3]) k[1])

> 
> 
