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RankDecomposition

Factors a rank-r matrix into {C, F}, where C holds the pivot columns and F the nonzero reduced-row-echelon rows, so that C.F equals the original matrix.

$ wo 'RankDecomposition[{{1, 2}, {2, 4}}]'
{{{1}, {2}}, {{1, 2}}}

$ wo 'RankDecomposition[{{1, 2, 3}, {4, 5, 6}}]'
{{{1, 2}, {4, 5}}, {{1, 0, -1}, {0, 1, 2}}}