Consider the matrix $\begin{bmatrix} 5 & -1 \\ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

1. Eigenvalue $3$ has a multiplicity of $2$, and only one independent eigenvector exists.
2. Eigenvalue $3$ has a multiplicity of $2$, and two independent eigenvector exist.
3. Eigenvalue $3$ has a multiplicity of $2$, and no independent eigenvector exists.
4. Eigenvalues are $3$ and $-3$, and two independent eigenvectors exist.