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Section 4: Using Matrix Operations
105
For example, let matrix A be
3X1(T
40
1
2
1
1 1
2
1 - 1
The HP-15C correctly calculates A'
1
to 10-digit accuracy as
-2
3 -1
3 - 4 2
-1
2 -1
Now let
so that
E =
10
20
0
0
o
io-
20
o
o
o
icr
20
3
1
2
1 1(T
40
1(T
40
2 10"
40
-10~
40
E is very near a singular matrix
S =
3 1 2
1 0 0
2 0 0
and ||E - S|| / ||E|| = V
3
X lO'
40
. This means that K(S) ^ 3 X 10
40
, so
it's not surprising that the calculated E""
1
E
-6.67 X10"
11
1
10"
10
0.8569
8.569 X 10
9
-4.284 X 10
9
0.07155
-4.284 X 10
9
2.142 X 10
9
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