Principles of Mathematics in Operations Research

238 Solutions

=> Hi =

16 - V208

M2 =

16 + V208

Then, ||yl(2)|| ||^(2)_1|| = 1.2676(15.2111) = 19.2815 = c[A(2)}.

We know, fi\ = j- and ji2 — j~- Consequently,

c[A(2)-^1 } = ^ = 19.2815 = AL = ^ = c[^( 2 )]

/^i IT Ai

(b) Take .4(3).

r i

i

2

1

L3

1

•2

1

3

1

4

1 I

3

1

4

1

5 J

4(3)

det(aJ - A{3)TA{3)) =

:3)rA(3) =

s_ 49

* 36

'49

36

3

4

21

. 40
3
4
3 „ 61
4 a 144
21
40 •3- s
10 *

3 21

4 40

61 3

144 10

3 769

10 3600

21

40

3

10

769

3600

= 0

(s - 3/415409)(s - 255/17041)(s - 1192/601) = 0 ;

v\ 415409' vi

255

17041 vz =

1192

60T

•c[A(3)M(3)] = ^ = vz

1192

(^601) = 274635.3
415409
det(s/ - A(3)) =
(^1) A A A
2 3
III
2 3 4
ill
3 4 5
= 0
Ai =
26
9675'
(s- 26/9675) (s
389
A 2 =
3180' Aa 529
389/3180)(s
745
Clearly, c[A(3)TA(3)} = (c[4(3)])^2.
c[A(3)]
745/529) = 0 =*•
^i = J{2£- = 524.0566
\ 2b 1
9675
(c) Take A(A).
m =
I l
4 5
I 1
5 6