True or false: Each matrix is row equivalent to one and only one reduced echelon matrix.
1
True.
Every matrix can be row reduced to an echelon form, and every echelon form can be further reduced to a unique reduced echelon form. The reduced echelon form may not be unique in terms of the entries that are non-zero, but the positions at which the non-zero entries occur are unique. Therefore, every matrix is row equivalent to one and only one reduced echelon matrix.
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