Let $\lambda_1$ and $\lambda_2$ be two distinct eigenvalues of an $n \times n$ matrix $A$, $v_1$ and $v_2$ are the corresponding eigenvectors. Prove that $v_1 + v_2$ is not an eigenvector of $A$.
Is this how you set this up? Unsure where to begin.
$A(v_1+v_2) = Av_1 + Av_2$
$A(v_1+v_2) = \lambda_1v_1 + \lambda_2v_2$