HP 49g+, Руководство пользователя, Страница: 354 / 862

Page 11-32
If you were performing these operations by hand, you would write the
following:










−
−
−
− ≅










−
−
−
− =
4
3
7
1 2 4
1 2 3
3 2 1
4
3
14
1 2 4
1 2 3
6 4 2
aug
A










− − −
≅










−
−
− −
− − ≅
32
3
7
13 6 0
1 1 0
3 2 1
32
24
7
13 6 0
8 8 0
3 2 1
aug
A










− −
≅
14
3
7
7 0 0
1 1 0
3 2 1
aug
A
The symbol
≅
(“ is equivalent to”) indicates that what follows is equivalent to
the previous matrix with some row (or column) operations involved.
The resulting matrix is upper-triangular, and equivalent to the set of equations
X +2Y+3Z = 7,
Y+ Z = 3,
-7Z = -14,
which can now be solved, one equation at a time, by backward substitution,
as in the previous example.
Gauss-Jordan elimination using matrices
Gauss-Jordan elimination consists in continuing the row operations in the
upper-triangular matrix resulting from the forward elimination process until an
identity matrix results in place of the original
A
matrix. For example, for the
case we just presented, we can continue the row operations as follows:
Multiply row 3 by –1/7:
7\Y 3 @RCI!
Multiply row 3 by –1, add it to row 2, replacing it:
1\ # 3
#2 @RCIJ!