1. **State the problem:** Find the eigenvectors of a given matrix $A$. 2. **Recall the definition:** Eigenvectors $\mathbf{v}$ satisfy the equation $$A\mathbf{v} = \lambda \mathbf{v}$$ where $\lambda$ is an eigenvalue. 3. **Find eigenvalues:** Solve the characteristic equation $$\det(A - \lambda I) = 0$$ to find eigenvalues $\lambda$. 4. **Find eigenvectors:** For each eigenvalue $\lambda$, solve $$(A - \lambda I)\mathbf{v} = \mathbf{0}$$ to find the eigenvectors $\mathbf{v}$. 5. **Example:** Since the matrix is not provided, the general method is as above. If you provide the matrix, I can compute the eigenvectors explicitly.