I have the following system:
\begin{equation} \begin{bmatrix} u \\ v \end{bmatrix} = \begin{bmatrix} xe^y \\ ye^x \end{bmatrix} \end{equation}
which is enclosed in an area given by $$ u = 1, u = e, v = 1, v = e$$
To be honest I am not even sure where to start, I would be thankful for any help.
For the first coordinate: we have $1\leq x e^x\leq e$. Take logarithms to get $0\leq\ln(x)+y\leq1$ which means that $y\geq-\ln(x)$ and $y\leq1-\ln(x)$. Similarly you'll get a sketch for the second coordinate; here we have $0\leq\ln(y)+x$ and $\ln(y)+x\leq1$, that is, $y\geq e^{-x}$ and $y\leq e^{1-x}$.
Now feel free to draw.
