Message Boards Message Boards

GROUPS:

[?] Reduced Row Echelon form

Posted 5 months ago
907 Views
|
3 Replies
|
2 Total Likes
|

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

3 Replies

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 5 months ago

Thank you for this answer Daniel. But what is a generic result?

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

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract