a11   a12   a13
a21   a22   a23
a31   a32   a33

a11=  !colonna 1
a21=
a31=

a12=  !colonna 2
a22=
a32=

a13=  !colonna 3
a23=
a33=

determinante=a11*(a22*a33-a23*a32)-a12*(a21*a33-a23*a31)+a13*(a21*a32-a22*a31)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

a11   a12   a13   a14
a21   a22   a23   a24
a31   a32   a33   a34
a41   a42   a43   a44

a11=  !colonna 1
a21=
a31=
a41=

a12=  !colonna 2
a22=
a32=
a42=

a13=  !colonna 3
a23=
a33=
a43=

a14=  !colonna 4
a24=
a34=
a44=

jt1= a11*(a22*(a33*a44-a34*a43)-a23*(a32*a44-a34*a42)+a24*(a32*a43-a33*a42))
jt2=-a12*(a21*(a33*a44-a34*a43)-a23*(a31*a44-a34*a41)+a24*(a31*a43-a33*a41))
jt3= a13*(a21*(a32*a44-a34*a42)-a22*(a31*a44-a34*a41)+a24*(a31*a42-a32*a41))
jt4=-a14*(a21*(a32*a43-a33*a42)-a22*(a31*a43-a33*a41)+a23*(a31*a42-a32*a41))

determinante=jt1+jt2+jt3+jt4

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

b11   b12   b13   b14  b15
b21   b22   b23   b24  b25
b31   b32   b33   b34  b35
b41   b42   b43   b44  b45
b51   b52   b53   b54  b55


b11   
     b22   b23   b24  b25
     b32   b33   b34  b35
     b42   b43   b44  b45
     b52   b53   b54  b55
jt1= b22*(b33*(b44*b55-b45*b54)-b34*(b43*b55-b45*b53)+b35*(b43*b54-b44*b53))
jt2=-b23*(b32*(b44*b55-b45*b54)-b34*(b42*b55-b45*b52)+b35*(b42*b54-b44*b52))
jt3= b24*(b32*(b43*b55-b45*b53)-b33*(b42*b55-b45*b52)+b35*(b42*b53-b43*b52))
jt4=-b25*(b32*(b43*b54-b44*b53)-b33*(b42*b54-b44*b52)+b34*(b42*b53-b43*b52))
dt1=b11*(jt1+jt2+jt3+jt4)

     -b12
b21         b23   b24  b25
b31         b33   b34  b35
b41         b43   b44  b45
b51         b53   b54  b55
jt1= b21*(b33*(b44*b55-b45*b54)-b34*(b43*b55-b45*b53)+b35*(b43*b54-b44*b53))
jt2=-b23*(b31*(b44*b55-b45*b54)-b34*(b41*b55-b45*b51)+b35*(b41*b54-b44*b51))
jt3= b24*(b31*(b43*b55-b45*b53)-b33*(b41*b55-b45*b51)+b35*(b41*b53-b43*b51))
jt4=-b25*(b31*(b43*b54-b44*b53)-b33*(b41*b54-b44*b51)+b34*(b41*b53-b43*b51))
dt2=-b12*(jt1+jt2+jt3+jt4)

            b13 
b21   b22         b24  b25
b31   b32         b34  b35
b41   b42         b44  b45
b51   b52         b54  b55
jt1= b21*(b32*(b44*b55-b45*b54)-b34*(b42*b55-b45*b52)+b35*(b42*b54-b44*b52))
jt2=-b22*(b31*(b44*b55-b45*b54)-b34*(b41*b55-b45*b51)+b35*(b41*b54-b44*b51))
jt3= b24*(b31*(b42*b55-b45*b52)-b32*(b41*b55-b45*b51)+b35*(b41*b52-b42*b51))
jt4=-b25*(b31*(b42*b54-b44*b52)-b32*(b41*b54-b44*b51)+b34*(b41*b52-b42*b51))
dt3=b13*(jt1+jt2+jt3+jt4)

                 -b14
b21   b22   b23        b25
b31   b32   b33        b35
b41   b42   b43        b45
b51   b52   b53        b55
jt1= b21*(b32*(b43*b55-b45*b53)-b33*(b42*b55-b45*b52)+b35*(b42*b53-b43*b52))
jt2=-b22*(b31*(b43*b55-b45*b53)-b33*(b41*b55-b45*b51)+b35*(b41*b53-b43*b51))
jt3= b23*(b31*(b42*b55-b45*b52)-b32*(b41*b55-b45*b51)+b35*(b41*b52-b42*b51))
jt4=-b25*(b31*(b42*b53-b43*b52)-b32*(b41*b53-b43*b51)+b33*(b41*b52-b42*b51))
dt4=-b14*(jt1+jt2+jt3+jt4)

                       b15
b21   b22   b23   b24
b31   b32   b33   b34
b41   b42   b43   b44
b51   b52   b53   b54

jt1= b21*(b32*(b43*b54-b44*b53)-b33*(b42*b54-b44*b52)+b34*(b42*b53-b43*b52))
jt2=-b22*(b31*(b43*b54-b44*b53)-b33*(b41*b54-b44*b51)+b34*(b41*b53-b43*b51))
jt3= b23*(b31*(b42*b54-b44*b52)-b32*(b41*b54-b44*b51)+b34*(b41*b52-b42*b51))
jt4=-b24*(b31*(b42*b53-b43*b52)-b32*(b41*b53-b43*b51)+b33*(b41*b52-b42*b51))
dt4= b15*(jt1+jt2+jt3+jt4)

!Formula:

b11=  !colonna 1
b21=
b31=
b41=
b51=

b12=  !colonna 2
b22=
b32=
b42=
b52=

b13=  !colonna 3
b23=
b33=
b43=
b53=

b14=  !colonna 4
b24=
b34=
b44=
b54=

b15=  !colonna 5
b25=
b35=
b45=
b55=

jt1= b22*(b33*(b44*b55-b45*b54)-b34*(b43*b55-b45*b53)+b35*(b43*b54-b44*b53))
jt2=-b23*(b32*(b44*b55-b45*b54)-b34*(b42*b55-b45*b52)+b35*(b42*b54-b44*b52))
jt3= b24*(b32*(b43*b55-b45*b53)-b33*(b42*b55-b45*b52)+b35*(b42*b53-b43*b52))
jt4=-b25*(b32*(b43*b54-b44*b53)-b33*(b42*b54-b44*b52)+b34*(b42*b53-b43*b52))
dt1= b11*(jt1+jt2+jt3+jt4)

jt1= b21*(b33*(b44*b55-b45*b54)-b34*(b43*b55-b45*b53)+b35*(b43*b54-b44*b53))
jt2=-b23*(b31*(b44*b55-b45*b54)-b34*(b41*b55-b45*b51)+b35*(b41*b54-b44*b51))
jt3= b24*(b31*(b43*b55-b45*b53)-b33*(b41*b55-b45*b51)+b35*(b41*b53-b43*b51))
jt4=-b25*(b31*(b43*b54-b44*b53)-b33*(b41*b54-b44*b51)+b34*(b41*b53-b43*b51))
dt2=-b12*(jt1+jt2+jt3+jt4)

jt1= b21*(b32*(b44*b55-b45*b54)-b34*(b42*b55-b45*b52)+b35*(b42*b54-b44*b52))
jt2=-b22*(b31*(b44*b55-b45*b54)-b34*(b41*b55-b45*b51)+b35*(b41*b54-b44*b51))
jt3= b24*(b31*(b42*b55-b45*b52)-b32*(b41*b55-b45*b51)+b35*(b41*b52-b42*b51))
jt4=-b25*(b31*(b42*b54-b44*b52)-b32*(b41*b54-b44*b51)+b34*(b41*b52-b42*b51))
dt3= b13*(jt1+jt2+jt3+jt4)

jt1= b21*(b32*(b43*b55-b45*b53)-b33*(b42*b55-b45*b52)+b35*(b42*b53-b43*b52))
jt2=-b22*(b31*(b43*b55-b45*b53)-b33*(b41*b55-b45*b51)+b35*(b41*b53-b43*b51))
jt3= b23*(b31*(b42*b55-b45*b52)-b32*(b41*b55-b45*b51)+b35*(b41*b52-b42*b51))
jt4=-b25*(b31*(b42*b53-b43*b52)-b32*(b41*b53-b43*b51)+b33*(b41*b52-b42*b51))
dt4=-b14*(jt1+jt2+jt3+jt4)

jt1= b21*(b32*(b43*b54-b44*b53)-b33*(b42*b54-b44*b52)+b34*(b42*b53-b43*b52))
jt2=-b22*(b31*(b43*b54-b44*b53)-b33*(b41*b54-b44*b51)+b34*(b41*b53-b43*b51))
jt3= b23*(b31*(b42*b54-b44*b52)-b32*(b41*b54-b44*b51)+b34*(b41*b52-b42*b51))
jt4=-b24*(b31*(b42*b53-b43*b52)-b32*(b41*b53-b43*b51)+b33*(b41*b52-b42*b51))
dt4= b15*(jt1+jt2+jt3+jt4)

determinante=dt1+dt2+dt3+dt4+dt5