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

> M[red]:=(A*E/l)*matrix(4,4,[1,0,-1,0,  0,1,0,0,  
> -1,0,1+1/2/sqrt(2),-1/2/sqrt(2),   0,0,-1/2/sqrt(2),1+1/2/sqrt(2)]);
> DET:=det(M[red]);

                         [ 1    0       -1          0    ]
                         [                               ]
                         [ 0    1       0           0    ]
                         [                               ]
                         [                1/2        1/2 ]
                         [               2          2    ]
                     A E [-1    0    1 + ----     - ---- ]
                         [                4          4   ]
                         [                               ]
                         [               1/2          1/2]
                         [              2            2   ]
                         [ 0    0     - ----     1 + ----]
                         [               4            4  ]
           M[red] := -------------------------------------
                                       l


                                  4  4  1/2
                                 A  E  2
                          DET := ----------
                                       4
                                    4 l

> F:=vector([F3[x], F3[y], F4[x], F4[y]]);

                  F := [F3[x], F3[y], F4[x], F4[y]]

> delta:=linsolve(M[red],F):convert(delta,matrix):
> delta[1]:=delta[1];delta[2]:=delta[2];

                1/2
  delta[1] := (2    + 1) l

                   1/2                              1/2
        (-F4[y] - 2    F4[x] + 2 F3[x] + 3 F4[x] + 2    F4[y])/(A E)


                                     F3[y] l
                         delta[2] := -------
                                       A E

> delta[3]:=delta[3];delta[4]:=delta[4];

  delta[3] :=

                1/2                      1/2
            (2 2    + 1) l (7 F3[x] + 2 2    F4[y] + 7 F4[x] - F4[y])
        1/7 ---------------------------------------------------------
                                       A E


                            l (F3[x] + F4[x] + F4[y])
                delta[4] := -------------------------
                                       A E

> f:=vector([X,0,0,0]);

                          f := [X, 0, 0, 0]

> delta:=vector([u[3],v[3],u[4],v[4]]);

                  delta := [u[3], v[3], u[4], v[4]]

> delta:=linsolve(M[red],f);

                 [    1/2                  1/2              ]
                 [2 (2    + 1) X l     (2 2    + 1) X l  X l]
        delta := [----------------, 0, ----------------, ---]
                 [      A E                  A E         A E]

> 
