Relative Property (T) and the Vanishing of the first ${\mathrm{\ell }}^2$-Betti number

In this paper, we show that certain families with relative property (T) have trivial first ${\mathrm{\ell }}^2$-Betti number. We apply this to the elementary matrix group ${\text{EL}}_n(\mathbb{R})$ where $\mathbb{R}$ is any countable unital ring of characteristic 0.