If I have a $2 \times 2$ matrix $A$, and then I find two eigenvalues $\lambda_1$ and $\lambda_2$ by subtracting $λI$ from $A$ and then taking the determinant=0(singular); to find $\lambda_1$ and $\lambda_2$.
So for a one eigenvalue $\lambda_1$, how many possibilities are there for eigenvectors? in another words, how many solutions are there?