Principles of Mathematics in Operations Research

(Rick Simeone) #1
236 Solutions

A-j = ReQe =

A7 = Q7R7, where

166.4231 0 0 0
0 7.7768 0 0
0 -0.0002 1.0218 0.0001
0 0 0.0001 0.2447
0
0

0 0.0321

0
0
0
0
1

0
0
0
0
0
0 0 0.0016

Qr =

R7

-1.0000
0-
0
0
0
0

"-166.4231
0
0
0
0
0

1jQr =

0
1.0000
0-
0-
0
0

0
-7.7768
0
0
0
0

"166.4231

0
0

0
0
1.0000 0.0001
0.0001 -1.0000
0
0

0
0.0002

0 0
0 0
0 0
0 0
0 -1.0000 0
0

0
0
-1.0218 -0.0001

0
0 7.7768
0
0
0
0

0 -0.2447
0
0

0
0
0 1.0218
0
0
0

0-
0

0
0
0
0 0.2447
0
0

0 1.0000

0 0
0 0
0 0
0 0
0.0321 0
0 0.0016

0 0
0 0
0 0
0 0
0 0.0321 0
0 0 0.0016

The diagonal entries are the eigen values of A.

6.3 (a) Take .4(2).


1.

[A(2)\h] =

<-)•

i = A(2

A(2) =

1

ill

10

.2 3T^1

"10 4-6"
0 lj—6 12

)"^16 / =

4
-6

1 1

. 2 3 _


<->

"l || 1 0"
0 ^l-^1 1
y 12I 2^1.

= [h\A(2)-\

-6'
12

"1.0"
0.5 =

1"
0
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