Transformation To Row Echelon Form
By means of a finite sequence of elementary row operations, called Gaussian elimination, any matrix can be transformed to row echelon form. Since elementary row operations preserve the row space of the matrix, the row space of the row echelon form is the same as that of the original matrix.
The resulting echelon form is not unique; for example, any multiple of a matrix in echelon form is also in echelon form. However, it is the case that every matrix has a unique reduced row echelon form. This means that the nonzero rows of the reduced row echelon form are the unique reduced row echelon generating set for the row space of the original matrix.
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