The Pivot(A, i, j) function pivots A about the non-zero entry A[i, j]. Multiples of the ith row are added to every other row in A, with the result that all of the entries in the jth column of A are zero except for the (i, j)th element.

The Pivot(A, i, j, L) function acts like Pivot(A, i, j) except that only rows indicated in L are modified. Rows not included in L are unaffected. If any rows in L are repeated or if i occurs in L, they are ignored. For more information regarding parameter L, see Matrix and Vector Entry Selection.

The inplace option (ip) determines where the result is returned. If given as inplace=true, the result overwrites the first argument. If given as inplace=false, or if this option is not included in the calling sequence, the result is returned in a new Matrix.

The condition inplace=true can be abbreviated to inplace.

The inplace option must be used with caution since, if the operation fails, the original Matrix argument may be corrupted.

The constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Matrix constructor that builds the result. These options may also be provided in the form outputoptions=[...], where [...] represents a Maple list.  If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order).

The inplace and constructor options are mutually exclusive.

This function is part of the LinearAlgebra package, and so it can be used in the form Pivot(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[Pivot](..).

$\mathrm{with}\left(\mathrm{LinearAlgebra}\right)\:$

$A≔⟨⟨1\,5\,9\,3\,7⟩\left|⟨2\,6\,0\,4\,8⟩\right|⟨3\,7\,1\,5\,9⟩|⟨4\,8\,2\,6\,0⟩⟩$

$A≔\left[\begin{array}{cccc}1& 2& 3& 4\\ 5& 6& 7& 8\\ 9& 0& 1& 2\\ 3& 4& 5& 6\\ 7& 8& 9& 0\end{array}\right]$

$A≔\mathrm{Pivot}\left(A\,2\,1\right)$

$A≔\left[\begin{array}{cccc}0& \frac{4}{5}& \frac{8}{5}& \frac{12}{5}\\ 5& 6& 7& 8\\ 0& -\frac{54}{5}& -\frac{58}{5}& -\frac{62}{5}\\ 0& \frac{2}{5}& \frac{4}{5}& \frac{6}{5}\\ 0& -\frac{2}{5}& -\frac{4}{5}& -\frac{56}{5}\end{array}\right]$

$A≔\mathrm{Pivot}\left(A\,1\,2\,\left[4..-1\,3\right]\right)$

$A≔\left[\begin{array}{cccc}0& \frac{4}{5}& \frac{8}{5}& \frac{12}{5}\\ 5& 6& 7& 8\\ 0& 0& 10& 20\\ 0& 0& 0& 0\\ 0& 0& 0& \mathrm{-10}\end{array}\right]$