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Pivoting

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For a linear system $ Ax=b$, a permutation of rows of the matrix changes the right-hand side:

$\displaystyle A(I,;)x = b(I). $

Contrary to that, a permutation of columns changes the solution:

$\displaystyle A(:,I) x(I) = b \,. $

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  automatically generated 3/ 8/2007