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e., the column rank of the) have to be at least as big as r. This proves that row rank of the is not any more substantial in comparison to the column rank of the. Now utilize this end result for the transpose of A to get the reverse inequality and conclude as during the former proof.

The point that the column and row ranks of any matrix are equivalent forms is fundamental in linear algebra. Many proofs happen to be provided. One of the most elementary kinds has become sketched in § Rank from row echelon kinds. Here's a variant of the proof:

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