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Then, for this particular example, in RPN mode, use:
[2,-1,41]
`
[[1,2,3],[2,0,3],[8,16,-1]]
`/
The calculator shows an augmented matrix consisting of the coefficients matrix
A
and the identity matrix
I
, while, at the same time, showing the next
procedure to calculate:
L2 = L2-2
⋅
L1 stands for “replace row 2 (L2) with the operation L2 – 2
⋅
L1. If we
had done this operation by hand, it would have corresponded to:
2\#1#1
@RCIJ
. Press
@@@OK@@@
, and follow the operations in
your calculator’s screen. You will see the following operations performed:
L3=L3-8
⋅
L1, L1 = 2
⋅
L1--1
⋅
L2, L1=25
⋅
L1--3
⋅
L3, L2 = 25
⋅
L2-3
⋅
L3,
and finally a message indicating “Reduction result” showing:
When you press
@@@OK@@@
, the calculator returns the final result [1 2 –1].
Calculating the inverse matrix step-by-step
The calculation of an inverse matrix can be considered as calculating the
solution to the augmented system [
A
|
I
]. For example, for the matrix
A
used
in the previous example, we would write this augmented matrix as
.
1
0
0
0
1
0
0
0
1
1
2
4
1
2
3
3
2
1
)
(
−
−
=
I
aug
A