The rank of a matrix is equal to the number of
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The rank of a matrix is equal to the number of non-zero of columns
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The rank of a matrix A is the number of leading entries in a row reduced form R for A. This also equals the number of nonrzero rows in R. For any system with A as a coefficient matrix, rank[A] is the number of leading variables. Now, two systems of equations are equivalent if they have exactly the same solution set.
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