Gear scheme for heat equation

Question

I have the following finite difference approximation to the standard 1D heat equation. $$ \dfrac{3u_j^{n+1} - 4u_j^n + u_j^{n-1}}{2\Delta t} - \alpha\dfrac{u_{j-1}^{n+1} - 2u_j^{n+1} + u_{j+1}^{n+1}}{\Delta x^2} = 0. $$ Then I set $$ U^n= \begin{pmatrix}u^{n}\\ u^{n-1}\end{pmatrix}. $$ I don'n know how to prove the existence of a matrix $A$ such that $$ U^{n+1}=AU^n. $$