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Replacement:
Replace a row by adding it to (or subtract from it) a multiple of the other row. For a given row ri, this is written as
ri - srj → ri
Note that when replacing row ri, nothing is multiplied by it. Rather, row rj is multiplied by a scalar s (that could be a fraction) and which is added to or subtracted from row ri.
7.13
Forward elimination: In forward elimination, we want to obtain a 0 in the a 21 position. To accomplish this, we can alter the second line in the matrix by subtracting from it
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