In pictures provided i understand the pivot column is column 2 and pivot row is row 3.
What I don't get is why its $0.25(4R_1 +29R_3)$ and not just $4R_1 +29R_3$.
Isn't the goal to get zeros in column 2 apart from pivot?
Thanks
2026-03-26 06:17:33.1774505853
Simplex Method Row Operations
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I don't think it would make such a major difference. They are just trying to zero out that entry in the first row, and the simplest way of doing that is $$ R_1 \leftarrow R_1 + 29/4 R_3 = 4/4R_1+29/4R_3 = \frac{4R_1+29R_3}{4} $$ They use the left-most flavor and you found the right-most simpler, ignoring the denominator since the entry is zeroed out anyhow.
I find yours more intuitive, but theirs is procedurally simpler.