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[?] Reduced Row Echelon form

Bert Aerts
Posted 4 years ago

Hi,

Mathematica 12 produces:

m = {{1 , 3, 4, b1}, {-4, 2, -6, b2}, {-3, -2, -7, b3}}
RowReduce[m]
{{1, 0, 13/7, 0}, {0, 1, 5/7, 0}, {0, 0, 0, 1}}

Wolfram Alpha produces the expected result with the variables b1,b2 and b3 in the result

rowechelen.png

How should I interprete the result from Mathematica, why 2 different results?

Kind regards, Bert
POSTED BY: Bert Aerts
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Bert Aerts
Bert Aerts
Posted 4 years ago

Thank you for this answer Daniel. But what is a generic result?
POSTED BY: Bert Aerts

A generic result is one that holds for almost all values of the parameters (in the measure theory sense of the term).
POSTED BY: Daniel Lichtblau

RowReduce in the Wolfram Language gives generic results. W|A makes more of an effort at what might, only partly facetiously, be termed "mind reading". One can achieve a similar effect using Reduce.

mat = {{1, 3, 4, b1}, {-4, 2, -6, b2}, {-3, -2, -7, b3}};
vars = Array[x, 3];
lhs = mat[[All, 1 ;; -2]]
rhs = Map[Last, mat]

(* Out[17]= {{1, 3, 4}, {-4, 2, -6}, {-3, -2, -7}}

Out[18]= {b1, b2, b3} *)

Reduce[lhs.vars == rhs, vars]

(* Out[19]= b1 == b2/2 - b3 && 
 x[2] == (7 b2)/26 - (3 b3)/13 + (5 x[1])/13 && 
 x[3] == -(b2/13) - b3/13 - (7 x[1])/13 *)
POSTED BY: Daniel Lichtblau
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