# HP 50g User Manual Page 360

Graphing calculator.

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