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Rank of a Matrix

 The rank of a matrix is the maximum number of linearly independent row vectors of the matrix.

A matrix (A1) is said to be row equivalent to a matrix (A2) if A1 can be obtained from A2 by carrying out elementary row operations. The row equivalent matrices have the same rank. The rank of a matrix doesn't change under elementary row operations.

Once the matrix is in row-echelon form, the number of nonzero rows can be counted, which is precisely the rank of the matrix.

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