The Chemistry Maths Book, Second Edition

(Grace) #1

Solutions to exercises 649


20.For


(i)E


1

1 = 1 α 1 + 1 φβ,E


2

1 = 1 α 1 + 1 (φ 1 − 1 1)β,


E


3

1 = 1 α 1 − 1 (φ 1 − 1 1)β,E


1

1 = 1 α 1 − 1 φβ


(ii)



  1. (ii)


(iii)e.g.



  1. (iii)right:


left:


Section 19.4



  1. (i) , (ii)

  2. (i) ,


(ii)



  1. (i)


(ii)D=










20


04


XX=











=












1


2


11


11


1


2


11


11


1

,


00 0


032 0


0032 −














11 1


02 2


11 1





























100


010


003


101


101


111















λ


22

3


1


5


1


2


==










,y


λ


11

2


0


1


==










,;y


λ


22

3


1


0


==










,x


λ


11

2


1


5


2


1


==











,;x


1


2


1


1


0


1


6


1


1


2















,















1


3


1


1


1














xx


34

1


1


1


1


=


















=












cc


φ


φ


φ


φ


,










xx


12

1


1


1


1


=
















=














cc


φ


φ


φ


φ


,








,


φφ=+(), ()512 1 2 2c= +



  1. (i)


(ii)



  1. (i) ,


(ii)



  1. (i) ,


(ii)


Section 19.5


















33.Q 1 = 1 (a 1 + 1 b)y


1

2

1 + 1 (a 1 − 1 b)y


2

2

,


y


y


xy


xy


1

2

1


2














=















Qy y


y


y


xx


x


=+ =



















416


1


2


3


1

2

2

2

1

2

12

1

,


33


2

x










xyz


x


y


z


()



−−


−−























321


213


132







xy


x


y


()


















02


20


xy


x


y


()



−−


















51


13


D=



















00 0


032 0


00 32


X



=


















1

1


2


1


2


1


2


1


2


1


2


1


2


1


2


1


2


0


X=


















1


2


1


2


1


2


1


2


1


2


1


2


1


2


1


2


0


D=















100


010


003


X



=
















1

1


2


110


202


110


X=−














101


101


111


D=










10


04


XX=












=












2


5


1


2


1


5


1


2


1

1


3


55


222


,







Free download pdf