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Let $V$ be an n-dimensional vector space and let $T:V\rightarrow V$ be a linear transformation such that 

$$Rank\:T \leq Rank\:T^{3}$$.

Then which one of the following statements is necessarily true?

  1. Null space$(T)$ = Range$(T)$
  2. Null space$(T)$ $\cap$ Range$(T)$={$0$}
  3. There exists a nonzero subspace $W$ of $V$ such that Null space$(T)$ $\cap$ Range$(T)$=$W$
  4. Null space$(T)$ $\subseteq$ Range$(T)$
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