A linear representability of group $G_{n,k,l}=\langle a,t;\ a^n=1,\ t^{-1}a^k t=a^l\rangle$

It is shown that the group $G_{n,k,l}=\langle a,t;\ a^n =1,\ t^{-1}a^kt=a^l\rangle$, where $n\neq0,k,l$ are integers, has faithful linear representation over a field of characteristic 0. An algoritm for explicit constructing of faithful linear representations of such groups is obtained.