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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,
.
12
3
0
1
2
5
2
1
2
1
2
1
−
−
−
−
=
aug
A
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]]
AAUG
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.