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I heard from multiple sources that to obtain the rank of a matrix A, you must first do row reduction to get the row reduced echelon form of matrix A and count the number of non zero rows.

But then there are other sources that say i must use row reduction to get matrix A to ROW ECHELON FORM, and not row reduced echelon form.

So which is it? should i transform matrix A to row echelon form or row reduced echelon form to find the rank?

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  • $\begingroup$ Row echelon form is enough. You only have to count the number of non-zero rows in the row echelon form. $\endgroup$ – Bergson Nov 4 '17 at 1:30
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As soon as you have changed your matrix into triangular form, you know the rank of the matrix. The reduced row echelon form is a more complete row reduction, which yields the explicit solutions of a linear system.

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