The nonzero ajoints are delta(4,1), delta(5,2), delta(6,1), and delta(4,2)-del\
ta(6,3)

Hence delta(4,2) and delta(6,3) are adjoint related

phi:=

[b(1,1)    0       0            0                0               0      ]
[                                                                       ]
[  0     b(2,2)    0            0                0               0      ]
[                                                                       ]
[b(3,1)  b(3,2)  b(3,3)         0                0               0      ]
[                                                                       ]
[b(4,1)  b(4,2)    0      b(2,2)*b(1,1)          0               0      ]
[                                                                       ]
[                                                2                      ]
[b(5,1)  b(5,2)  b(5,3)   - b(4,1)*b(2,2)  b(2,2) *b(1,1)        0      ]
[                                                                       ]
[b(6,1)  b(6,2)  b(6,3)   b(3,2)*b(1,1)          0         b(3,3)*b(1,1)]


                2       4       4
det(phi):=b(3,3) *b(2,2) *b(1,1)

delta:=

[   0        0        0        0     0  0]
[                                        ]
[   0        0        0        0     0  0]
[                                        ]
[xi(3,1)  xi(3,2)     0        0     0  0]
[                                        ]
[   0        0        0        0     0  0]
[                                        ]
[xi(5,1)     0     xi(5,3)     0     0  0]
[                                        ]
[   0     xi(6,2)  xi(6,3)  xi(3,2)  0  0]


We denote this delta by the shortform

shortformdelta:={xi(3,1),

                 xi(3,2),

                 ss,

                 xi(5,1),

                 xi(5,3),

                 ss,

                 xi(6,2),

                 xi(6,3)}

deltaprime:=phi*delta*phi**(-1)$

******* Suppose xi(3,1) = 0 and xi(3,2) = 0 and xi(5,3)=0$

phi*delta*phi**(-1):=
mat((0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(0,0,0,0,0,0),(b(2,2)**2*xi(5,1),0
,0,0,0,0),( - b(3,1)*xi(6,3),(b(1,1)*(b(3,3)*xi(6,2) - b(3,2)*xi(6,3)))/b(2,2),b
(1,1)*xi(6,3),0,0,0))$

deltaprime(3,1):=0$

deltaprime(3,2):=0$

deltaprime(5,1):=b(2,2)**2*xi(5,1)$

deltaprime(5,3):=0$

deltaprime(6,2):=(b(1,1)*(b(3,3)*xi(6,2) - b(3,2)*xi(6,3)))/b(2,2)$

deltaprime(6,3):=b(1,1)*xi(6,3)$