${x}_{n+1}=2{y}_{n}-{z}_{n}$

${y}_{n+1}={y}_{n}$

${z}_{n+1}={x}_{n}-2{y}_{n}+2{z}_{n}$

What is the solution in general for ${x}_{0}$, ${y}_{0}$, ${z}_{0}$ arbitrary?

It is intended to be solved using Jordan Normal Form of the Linear Algebra knowledge. I have no idea how to start, can anyone give a hint?