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linalg(deprecated)

 pivot
 pivot about a matrix entry

 Calling Sequence pivot(A, i, j) pivot(A, i, j, r..s)

Parameters

 A - matrix i, j - positive integers r..s - range of rows to be pivoted

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\mathrm{matrix}\left(4,4,\left[1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6\right]\right)$
 ${A}{≔}\left[\begin{array}{cccc}{1}& {2}& {3}& {4}\\ {5}& {6}& {7}& {8}\\ {9}& {0}& {1}& {2}\\ {3}& {4}& {5}& {6}\end{array}\right]$ (1)
 > $A≔\mathrm{pivot}\left(A,2,1\right)$
 ${A}{≔}\left[\begin{array}{cccc}{0}& \frac{{4}}{{5}}& \frac{{8}}{{5}}& \frac{{12}}{{5}}\\ {5}& {6}& {7}& {8}\\ {0}& {-}\frac{{54}}{{5}}& {-}\frac{{58}}{{5}}& {-}\frac{{62}}{{5}}\\ {0}& \frac{{2}}{{5}}& \frac{{4}}{{5}}& \frac{{6}}{{5}}\end{array}\right]$ (2)
 > $A≔\mathrm{pivot}\left(A,3,2\right)$
 ${A}{≔}\left[\begin{array}{cccc}{0}& {0}& \frac{{20}}{{27}}& \frac{{40}}{{27}}\\ {5}& {0}& \frac{{5}}{{9}}& \frac{{10}}{{9}}\\ {0}& {-}\frac{{54}}{{5}}& {-}\frac{{58}}{{5}}& {-}\frac{{62}}{{5}}\\ {0}& {0}& \frac{{10}}{{27}}& \frac{{20}}{{27}}\end{array}\right]$ (3)