HP 50G

Page 11-42
LINSOLVE([X-2*Y+Z=-8,2*X+Y-2*Z=6,5*X-2*Y+Z=-12],
[X,Y,Z])
to produce the solution: [X=-1,Y=2,Z = -3].
Function LINSOLVE works with symbolic expressions. Functions REF, rref, and
RREF, work with the augmented matrix in a Gaussian elimination approach.
Functions REF, rref, RREF
The upper triangular form to which the augmented matrix is reduced during the
forward elimination part of a Gaussian elimination procedure is known as an
"echelon" form. Function REF
(Reduce to Echelon Form) produces such a matrix
given the augmented matrix in stack level 1.
Consider the augmented matrix,
Representing a linear system of equations, A⋅x = b, where
A = [[1,-2,1],[2,1,-2],[5,-2,1]],
and
b = [[0],[-3],[12]].
Enter the augmented matrix, and save it into variable AAUG, in ALG mode:
[[1,-2,1,0],[2,1,-2,-3][5,-2,1,12]]
 UG
Application of function REF produces:
The result is the upper triangular (echelon form) matrix of coefficients resulting
from the forward elimination step in a Gaussian elimination procedure.
.
12
3
0
125
212
121
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⎢
⎢
⎢
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−
−
−
−
=
aug
A