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# 4pgnotes - STEPS IN GAUSSIAN ELIMINATION The steps in...

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STEPS IN GAUSSIAN ELIMINATION The steps in Gaussian elimination can be summarized as follows: Stage 1: (Forward Elimination Phase) 1. Search the first column of [ A | b ] from the top to the bottom for the first non-zero entry, and then if necessary, the second column (the case where all the coefficients corresponding to the first variable are zero), and then the third column, and so on. The entry thus found is called the current pivot . 2. Interchange, if necessary, the row containing the current pivot with the first row. 3. Keeping the row containing the pivot (that is, the first row) untouched, subtract appropriate multiples of the first row from all the other rows to obtain all zeroes below the current pivot in its column. 4. Repeat the preceding steps on the submatrix consisting of all those elements which are below and to the right of the current pivot. 5. Stop when no further pivot can be found. Remark : The forward elimination phase of the Gauss elimination method leads to the row echelon form

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