1. **Problem Statement:** Show that the sequence $\{u_n\}$ satisfies the recurrence relation $$u_n = -3u_{n-1} + 4u_{n-2}.$$\n\n2. **Understanding the recurrence relation:** This means for every term $u_n$ in the sequence, it can be expressed as a linear combination of the two preceding terms $u_{n-1}$ and $u_{n-2}$ with coefficients $-3$ and $4$ respectively.\n\n3. **Approach:** To show that $\{u_n\}$ is a solution, we need to verify that for all $n \geq 2$, the relation holds true. This usually involves either: \n- Substituting the given sequence terms into the relation and checking equality, or\n- Using initial conditions and induction if the sequence is explicitly defined.\n\n4. **Example verification:** Suppose the sequence $\{u_n\}$ is given or defined by initial terms $u_0$ and $u_1$. Then for $n=2$, check if $$u_2 = -3u_1 + 4u_0.$$\n\n5. **Inductive step:** Assume the relation holds for $n=k$ and $n=k-1$, then show it holds for $n=k+1$ by substituting and simplifying.\n\n6. **Conclusion:** If the above steps hold for all $n$, then $\{u_n\}$ is indeed a solution to the recurrence relation $$u_n = -3u_{n-1} + 4u_{n-2}.$$