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Let $A$ be an $n \times n$ real matrix. It is known that there are two distinct $n$-dimensional real column vectors $v_{1}, v_{2}$ such that $A v_{1}=A v_{2}$. Which of the following can we conclude about $A?$

  1. All eigenvalues of $A$ are non-negative.
  2. $A$ is not full rank.
  3. $A$ is not the zero matrix.
  4. $\operatorname{det}(A) \neq 0$.
  5. None of the above.
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