kill(all)$

Reduced row echelon from matrix , version  1.0
peter.vlasschaert@gmail.com,16/10/2019

?  How to find :Reduced row echelon from matrix ( = excel)
=============================================

see : internet
https://stackoverflow.com/questions/30693793/how-to-find-the-reduced-row-echelon-form-of-a-matrix-in-maxima

definition : rref(A)
------------------------

rref(a):=block([p,q,k],[p,q]:matrix_size(a),a:echelon(a),
    k:min(p,q),
    for i thru min(p,q) do 
    (if a[i,i]=0 then (k:i-1,return())),
    for i:k thru 2 step -1 do 
    (for j from i-1 thru 1 step -1 do 
        a:rowop(a,j,i,a[j,i])
    ),
    a)$

rem : several row operations to find final result

How to enter : Matrix 'A'
==================

Menu: Algebra:Entermatrix

example A: rows :2,columns:5
=======================
rows ≠ columns , 'doesn't work'

Dimension of the null space or nullity | Vectors and spaces | Linear Algebra | Khan Academy
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youtube :
=======

see :https://www.youtube.com/watch?v=abYAUqs_n6I

A: matrix(
 [1,1,2,3,2], 
 [1,1,3,1,4]
);

rref(A);

echelon(A);

rem : echelon () =rref()

example B: rows: 5,columns :5
========================
rows =columns , 'works'

B:matrix([12,-27,36,44,59],
          [26,41,-54,24,23],
          [33,70,59,15,-68],
          [43,16,29,-52,-61],
          [-43,20,71,88,11])$

example : see internet

rref(B);

echelon(B);

rem : echelon () ≠ rref()