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KarlJacobi (talk | contribs) →{{anchor|rref}}Reduced row echelon form: Small justification given of the permutation of columns indicated. |
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I & X\\ 0&0
\end{pmatrix},</math>
where {{mvar|I}} is the [[identity matrix]] of dimension <math>j</math> equal to the rank of the entire matrix, {{mvar|X}} is a matrix with <math>j</math> rows and <math>n-j</math> columns, and the two {{math|0}}'s are [[zero matrix|zero matrices]] of appropriate size. Since a permutation of columns is not a row operation, the resulting matrix is inequivalent under elementary row operations. In the Gaussian elimination method, this corresponds to a permutation of the unknowns in the original linear system that allows a linear parametrization of the row space, in which the first <math>j</math> coefficients are unconstrained, and the remaining <math>n-j</math> are determined as linear combinations of these.
== Systems of linear equations ==
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