We assume in this question only that $n = 2$. Determine $u(A)$ in the following case:
$$A = \begin{pmatrix} \alpha & \gamma \\ 0 & \beta \end{pmatrix}$$
where $\alpha, \beta$ and $\gamma$ are fixed real numbers with $\alpha \neq \beta$ and $\{\alpha, \beta\} \subset D_u$. We will express the coefficients of $u(A)$ in terms of $\alpha, \beta$ and $\gamma, U(\alpha)$ and $U(\beta)$.