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Mathematica has RowReduce[], how can I use this to calculate a basis for the range of any matrix?

Given

A={{1,1,1,1,2},{1,2,4,0,5},{2,1,-1,4,0},{-1,1,5,-1,2}};

RowReduce[A]=={{1,0,-2,0,1},{0,1,3,0,2},{0,0,0,1,-1},{0,0,0,0,0}}

The leading 1's in the reduced row echelon form select the first, second, and fourth column vectors of A as a basis for the range of A. How do I program mathematica to make that selection after calculating RowReduce[A]?

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Firstly, there is no such thing as the basis. Secondly, the range of a transformation is generated by the columns, so RowReduce[Transpose[M]] ought to do it.

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  • $\begingroup$ This is not what I had in mind at all. $\endgroup$ – Phillip Dukes Apr 14 '17 at 16:22
  • $\begingroup$ @PhillipDukes Do you always speak in riddles? $\endgroup$ – Igor Rivin Apr 14 '17 at 17:12
  • $\begingroup$ "This is not what I had in mind at all." - then @Phillip, can you come up with a formulation that won't confuse answerers? $\endgroup$ – J. M. is in limbo Apr 14 '17 at 18:31
  • $\begingroup$ @J.M. thank you, I hope my example is clear enough. $\endgroup$ – Phillip Dukes Apr 14 '17 at 20:32

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