HP 50g User Manual page 360

Multiply row 2 by –1/8: 8\Y2 @RCI!
Multiply row 2 by 6 add it to row 3, replacing it: 6#2#3 @RCIJ!
If you were performing these operations by hand, you would write the
following:
A
A
aug
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
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:
⎛
2 4
⎜
3 2
⎜
aug
⎜
4 2
⎝
⎛
1 2 3
⎜
0 8
⎜
⎜
0 6
⎝
A
aug
⎞ ⎛
6 14 1
⎟ ⎜
1 3 3
⎟ ⎜
⎟ ⎜
1 4 4
⎠ ⎝
⎞ ⎛
7 1
⎟ ⎜
8 24 0
⎟ ⎜
⎟ ⎜
13 32 0
⎠ ⎝
⎛ 1 2 3
⎜
0 1 1
⎜
⎜
0 0 7
⎝
X +2Y+3Z = 7,
Y+ Z = 3,
-7Z = -14,
⎞
2 3 7
⎟
2 1 3
⎟
⎟
2 1 4
⎠
2 3 7
1 1 3
6 13 32
7 ⎞
⎟
3
⎟
⎟
14
⎠
⎞
⎟
⎟
⎟
⎠
Page 11-33