Continuing to the Jacobian anyways, we arrive at
[itex]
J = \left[
\begin{array}{ccc}
1  (\bar{Y} + \bar{Z}) & \bar{X} & \bar{X} \\
a\bar{Y} & a\bar{X}1 & 0 \\
a\bar{Z} & 0 & a\bar{X}1
\end{array}
\right].
[/itex]
Plugging in what we know,
[itex]
J = \left[
\begin{array}{ccc}
a & \frac{1}{a} &\frac{1}{a} \\
a\bar{Y} & 0 & 0 \\
a\bar{Z} & 0 & 0
\end{array}
\right].
[/itex]
This means that the trace of the Jacobian is negative, i.e. [itex] tr(J) = a < 0 [/itex]. Also that the determinant is equal to zero. My book does not talk about what happens when the determinant of the Jacobian is zero. Any insights?
