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Student[LinearAlgebra]

 Pivot

 Calling Sequence Pivot(A, i, j, options)

Parameters

 A - Matrix i, j - integers; position of the pivot entry options - (optional) parameters; for a complete list, see LinearAlgebra[Pivot]

Description

 • The Pivot(A, i, j) command pivots A about the nonzero entry ${A}_{i,j}$.  Multiples of the ith row are added to every other row in A, with the result that all entries in the jth column of A are zero except for the $i,j$th element.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{LinearAlgebra}]\right):$
 > $A≔⟨⟨1,5,9,3⟩|⟨2,6,0,4⟩|⟨3,7,1,5⟩|⟨4,8,2,6⟩⟩$
 ${A}{≔}\left[\begin{array}{rrrr}{1}& {2}& {3}& {4}\\ {5}& {6}& {7}& {8}\\ {9}& {0}& {1}& {2}\\ {3}& {4}& {5}& {6}\end{array}\right]$ (1)
 > $P≔\mathrm{Pivot}\left(A,1,1\right)$
 ${P}{≔}\left[\begin{array}{rrrr}{1}& {2}& {3}& {4}\\ {0}& {-}{4}& {-}{8}& {-}{12}\\ {0}& {-}{18}& {-}{26}& {-}{34}\\ {0}& {-}{2}& {-}{4}& {-}{6}\end{array}\right]$ (2)
 > $\mathrm{Pivot}\left(P,2,2\right)$
 $\left[\begin{array}{rrrr}{1}& {0}& {-}{1}& {-}{2}\\ {0}& {-}{4}& {-}{8}& {-}{12}\\ {0}& {0}& {10}& {20}\\ {0}& {0}& {0}& {0}\end{array}\right]$ (3)