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The ultimate matrix (in decreased row echelon sort) has two non-zero rows and thus the rank of matrix A is 2.
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The reality that the column and row ranks of any matrix are equivalent varieties is elementary in linear algebra. Quite a few proofs are actually specified. One of the more elementary kinds has long been sketched in § Rank from row echelon sorts. Here's a variant of the evidence:
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Once in row echelon sort, the rank is clearly the exact same for both row rank and column rank, and equals the amount of pivots (or standard columns) in addition to the amount of non-zero rows.
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The solution is exclusive if and provided that the rank equals the amount of variables. In any other case the final Resolution has k absolutely free parameters the place k may be the difference between the quantity of variables as well as the rank. In this instance (and assuming the procedure of equations is in the true or complicated numbers) the technique of equations has infinitely numerous alternatives.
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