Is There a Simple Proof of the Nullity - Rank Theorem?

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A query about a simple proof for the Nullity-Rank Theorem, which states that for a linear transformation T: U->V, the equation rank(T) + Nullity(T) = n holds, initiates the discussion. A suggestion is made to refer to the Wikipedia page on the theorem, specifically highlighting the second proof provided there. This proof is considered satisfactory for addressing the initial question posed. The conversation emphasizes the importance of accessible resources for understanding mathematical concepts. Overall, the discussion points towards existing literature as a potential solution for those seeking clarity on the theorem.
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Is there a short and simple proof of the Nullity - Rank Theorem which claims that if T: U->V is a linear transformation then rank(T)+Nullity(T)=n where n is the n dimension vector space U.
 
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