HP -15C Advanced Functions Handbook page 111

Section 4: Using Matrix Operations 109
Substituting, you find
""1.00146
0.00146
EX- 0.00146
0.00146
0.00147
Upon checking (using I MATRIX] 7), you find that I/HE"
1
!! «
9.9 X 10~
5
, which is very small compared with ||E|| « 1.6 X 10
4
(or
that the calculated condition number is large — ||E|| HE"
1
!! *»
1.6 X10
8
).
Choose any row vector U
T
= (1, 1, 1, 1, 1) and calculate
u
T
E'
1
~ 10,073(1, 1,1,1,1).
Using a = W
v
T
=au
T
E~
l
« 1.0073 (1, 1, 1, 1, 1)
r
r
= (1,1, 1,1,1)
||r
T
E||«5Xl(r
4
||rl||E||«8X10
4
.
As expected, ||r
T
E|| is small compared with ||r
T
||||E||.
Now replace the first row of E by
10
7
r
T
E = (1000, 1000, 1000, 1000, 1000)
and the first row of B by 10
7
r
T
B = 10
7
. This gives a new system
equation AX — D, where
A =
1000 1000 1000 1000 1000
y x y y y
y y x y y
y y y x y
y y y y x
andD =
10
7
0
0
0
0