Answers to Selected Problems 801CHAPTER 13
13.1Before:X 1 =
{
17
13
}
,X 2 =
{
15
22
}
;After:X 1 ={
23
22
}
, X 2 =
{
9
13
}
13.3(a) 9, (b) 10, (c) 11 13.4 10 13.6(i j )=(i 4 ) 13.8x∗= 2
1 3.9x 1 ( 2 )= 2. 8297 , x 2 ( 2 )= 1. 9345 , x 3 ( 2 )= 1. 6362 , x 4 ( 2 )= 1. 1887
13.12Number of copies of strings 1, 2, 3, 4, 5, 6, 7 are 0, 0, 1, 2, 5, 2, 2, respectively
13.14String length= 37
CHAPTER 14
14.1c∗ 1 = 0. 04 , c∗ 2 = 0. 81
14.3(a){ 0. 001165 , 0. 002329 , 0. 03949 ,− 0. 05635 },
(b){ 0. 0009705 , 0. 001941 , 0. 05273 ,− 0. 084102 },
(c) { 0. 0009704 , 0. 001941 , 0. 05265 ,− 0. 08395 }
14.5
{
∂yi
∂x 1}
={− 0. 000582 ,− 0. 001165 ,− 0. 002329 , 0. 002329 }
14.7
{
∂yi
∂x 3}
={ 0. 4693 × 10 −^7 , 4770. 9 × 10 −^7 , − 0. 027948 , 0. 027947 }
14.9(a)
{
0. 000125
0. 000458
}
(b){
− 0. 000229
− 0. 000229
}
,
{
0. 0
0. 000333
}
(c)
{
− 275
0
}
,
{
0
200
}
14.11
∂λ 1
∂A 2= 2. 28840 ,
∂λ 2
∂A 2= 64. 8649 ,
∂Y 1
∂A 2
=
{
− 0. 312639 × 10 −^21
0 91666. 3 × 10 −^6
}
,
∂Y 2
∂A 2
=
{
0. 698492 × 10 −^8
0 83790. 8 × 10 −^2
}
1 4.15
∂ω 1
∂D= − 1. 584664 ,
∂ω 2
∂D= − 2. 744719
14.16y∗= 3 ,A∗ 1 = 0. 316228 × 10 −^7 , A∗ 2 = 0. 948683 × 10 −^7 , f∗= 0. 6 × 10 −^6
14.18y∗= 0. 25 , A 1 ∗= 1. 0 ,A∗ 2 = 1. 0 ,f∗= 34. 7565
14.20 X∗= { 0. 7635 , 1. 0540 }, f∗= 871 .5670 withf= 0. 625 f 1 + 0611. 0 f 2
14.21 X∗= { 0. 8 , 1. 1 }, F∗= 3. 1267
14.22 X∗= { 0. 75 , 1. 25 }