Representations of ${\mathbb{G}}_a⋊{\mathbb{G}}_m$ into $\mathrm{S}\mathrm{L}(3,k)$ in positive characteristic

Let $k$ be an algebraically closed field of positive characteristic $p$. In this article, we classify representations of ${\mathbb{G}}_a⋊{\mathbb{G}}_m$ into $\mathrm{S}\mathrm{L}(3,k)$, and thereby we classify fundamental representations of ${\mathbb{G}}_a$ into $\mathrm{S}\mathrm{L}(3,k)$.