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Suppose I need to define a matrix of the form

{{a, b, Reduce[a<b]}, {c, d, Reduce[c<d]}, {e, f, Reduce[e<f]}}

but with a lot more rows and automating the Reduce argument by making it be "first element of this row < second element of this row".

How would I do that? I understand the question doesn't make much sense in a coding grammar or optimization way, but I would like to learn how to evaluate "this row" in this sense.

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Assuming you have the matrix with the last column missing, you can Map or Apply over the individual rows of the matrix & add some new columns. Here are two possible approaches:

{##, Reduce[Less@##]} & @@@ {{a, b}, {c, d}, {e, f}}
(* {{a, b, b ∈ Reals && a < b}, {c, d, d ∈ Reals && c < d}, {e, f, f ∈ Reals && e < f}} *)
Append[#, Reduce[Less @@ #]] & /@ {{a, b}, {c, d}, {e, f}}
(* same output *)
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