Rees algebra and almost linearly presented ideals in three variables

Let R=[x,y,z] and I=(f₀,,fₙ₋₁) be a height two perfect ideal which is almost linearly presented (that is, all but the last column have linear entries, but the last column has entries which are homogeneous of degree $2$). Further we suppose that after modulo an ideal generated by two variables, the presentation matrix has rank one. Also, the ideal I satisfies 2 but not 3, then we obtain explicit formulas for the defining ideal of the Rees algebra (I) of I.