When looking for a possible new pivot, why do we only search from row k to n in column k? In other words, what unwanted thing could happen if we used a row above row k as the new pivot row?
am not really sure why, we choose the next pivot to be below the kth row, can someone explain mathematically why it works?
for example
\(\displaystyle \begin{bmatrix} 2 & 4 & -5 & 1 \\ 0 & 0 & -3 & 2 \\ 0 & 0 & -2 & 0 \\ 0 & 0 & -4 & 1 \end{bmatrix} \) so the current pivot entry is at 3,3 what would happen if I choose a pivot entry above it?
am not really sure why, we choose the next pivot to be below the kth row, can someone explain mathematically why it works?
for example
\(\displaystyle \begin{bmatrix} 2 & 4 & -5 & 1 \\ 0 & 0 & -3 & 2 \\ 0 & 0 & -2 & 0 \\ 0 & 0 & -4 & 1 \end{bmatrix} \) so the current pivot entry is at 3,3 what would happen if I choose a pivot entry above it?
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