Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[Pivot], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The function pivot pivots the matrix A about A[i, j] which must be non-zero.

The function pivot(A, i, j) will add multiples of the ith row to every other row in the matrix, with the result that the (k, j)th entry of the matrix A is set to zero for all k not equal to i. That is, the jth column of the matrix will be all zeros, except for the (i, j)th element.

The call pivot(A, i, j, r..s) acts like pivot(A, i, j) except that only rows r through s are set to zero in the jth column.  Rows not in the range r..s are not affected.

The command with(linalg,pivot) allows the use of the abbreviated form of this command.

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

$A≔\mathrm{matrix}\left(4\,4\,\left[1\,2\,3\,4\,5\,6\,7\,8\,9\,0\,1\,2\,3\,4\,5\,6\right]\right)$

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

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

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

$A≔\mathrm{pivot}\left(A\,3\,2\right)$

$A≔\left[\begin{array}{cccc}0& 0& \frac{20}{27}& \frac{40}{27}\\ 5& 0& \frac{5}{9}& \frac{10}{9}\\ 0& -\frac{54}{5}& -\frac{58}{5}& -\frac{62}{5}\\ 0& 0& \frac{10}{27}& \frac{20}{27}\end{array}\right]$