Principles of Mathematics in Operations Research

Solutions 217

Problems of Chapter 3

3.1

Vi = a

i>2 = a

A =

1

1

1

-1

-vi

12 0-1

1-13 2

1-13 2

-1 1-3 1

[a^1 a^2 a^3 a^4 ].

=> vfvi = 4, v~[a^2 = -1, v\a^3 = 9, vfa^4 = 2.

v 3 =a°

VT

2 V 2 —, t^cT = -9, v 2 a = --.

27

•27-W2 - -J-«i -

This result is acceptable since a^3 = 2a^1 — a^2 ; hence it is dependent on a^1 and

a^2.

4 2-^ -2^4

W 4 = a - -jf-^ - —Wi

T

Thus,

Qi

\\vi\

12

V2

\v 21

2

6

6

6 J

Qi

V4

Kl

o

_^

6

_^

6

3 J

a^1 = 2q\Vi

a^2 = -\qi + h&q2 = -\vi+v 2

a^3 = 2(2ft) - (-§(& + ^)<? 2 = |gi + ^% = 2Wl - «2

a^4 = qi - A/392 - \/65 4 = \vx + =£v 2 + vA

Q =

<£>

I ^ Q

2 2 u

1 \/3 \/6

2 6 6

1 y/3 y/6

2 6 6

1 y/3 V6

. 2 6 3.

, R =

r2 -i ^ n

L 2 2 X

0 3^3_3^3 _^

0 0 0 \/6