True or false: Each matrix is row equivalent to one and only one reduced echelon matrix.
1
True:
Each matrix can be transformed to one and only one reduced echelon form (REF) matrix through a series of row operations, such as swapping two rows, multiplying a row by a nonzero constant, or adding a multiple of one row to another row. The row operations used to transform the matrix to the REF are unique, and the resulting matrix is also unique. Therefore, each matrix is row equivalent to one and only one reduced echelon matrix.
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