Preform a Pivot Operation

Preform a Pivot Operation

Syntax B = Pivot(A, r, c)

Description
Performs a pivot operation on the Tableau A about row r and column c. Let

(

) be the number of rows (columns) in the matrix A. The output matrix B and the same number of rows and columns and for


 i = 1 , \ldots , m


 i \neq r


 j = 1 , \ldots , n


 \[


\begin{array}{rcl}


B_{r,j} & = & A_{r,j} \frac{1}{ A_{r,c} } 


\\


B_{i, j}  & = & A_{i,j} - A_{r,j} \frac{ A_{i,c} }{ A_{r, c} }


\end{array}


\]

It follows that


 \[


B_{i,c} =  \left\{ \begin{array}{ll}


     1 & {\rm if} \; i = r \\


     0 & {\rm otherwise}


\end{array} \right.


\]

Example
The section Pivot2_1 contains an example use of the Pivot function.

Matlab Source Code



function B = Pivot(A, r, c)




[m, n]     = size(A);


B          = zeros(m, n);


B(r, :)    = A(r, :) / A(r, c);


for i = 1 : m


     if i ~= r


          B(i, :) = A(i, :) - A(i, c) * B(r, :);


     end


end

Input File: Pivot.m