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sage: P.<b1,b2,b3> = QQ[]
sage: A = Matrix(P, 3, 4, [[1,1,2,b1], [1,0,1,b2], [2,1,3,b3]])
sage: A
[ 1  1  2 b1]
[ 1  0  1 b2]
[ 2  1  3 b3]
sage: A.echelon_form('row_reduction')
[            1             0             1            b2]
[            0             1             1       b1 - b2]
[            0             0             0 -b1 - b2 + b3]

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