9. Find all $a_{0} \in \mathbf{R}$, such that the sequence $a_{0}, a_{1}, \cdots$ determined by $a_{n+1}=2^{n}-3 a_{n}, n \in \mathbf{Z}^{+}$ is increasing.
9. When $n \in \mathbf{N}$, by repeatedly iterating $a_{n}=2^{n-1}-3 a_{n-1}$, we can obtain $a_{n}=\frac{2^{n}+(-1)^{n+1} 3^{n}}{5}+(-1)^{n} 3^{n} a_{0}$. This holds for $n=0$ as well. Furthermore, we can find
$d_{n}=a_{n}-a_{n-1}=\frac{2^{n-1}}{5}\left(1+4(-2)^{n+1}\left(\frac{3}{2}\right)^{n-1}\left(1-5 a_{0}\right)\right)$. If $1-5 a_{0}>0$, then for sufficiently large even $n$, $d_{n}>0$, meaning the sequence $\left\{a_{n}\right\}$ is increasing.