HP 50g User Manual page 369

LINSOLVE([X-2*Y+Z=-8,2*X+Y-2*Z=6,5*X-2*Y+Z=-12],
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
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]]
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.
[X,Y,Z])
⎡ 1 2
⎢
A
2 1
⎢
aug
⎢
5 2
⎣
b = [[0],[-3],[12]].
1 0 ⎤
⎥
3 .
2
⎥
⎥
1 12
⎦
UG
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