The Chemistry Maths Book, Second Edition

(Grace) #1

646 Solutions to exercises



  1. 6 8.− 4 9. 30

  2. (i)C


11

1 = 1 − 1 ,C


12

1 = 1 − 3 ,C


13

1 = 1 − 2


C


21

1 = 1 − 5 ,C


22

1 = 1 − 2 ,C


23

1 = 1 + 3


C


31

1 = 1 − 2 ,C


32

1 = 1 + 7 ,C


33

1 = 1 − 4


(ii)− 13


Section 17.3


11.− 6 12. 4 13. 0 14. 144


Section 17.4


15.x 1 = 1 y 1 = 1 z 1 = 10 16.w 1 = 1 x 1 = 1 y 1 = 1 1,z 1 = 1 − 1



  1. (ii)x 1 = 1 (z 1 + 1 3) 25 ,y 1 = 1 (7z 1 − 1 4) 2 5, all z

  2. (ii)x 1 = 1 z 2 3,y 1 = 1 − 2 z 2 3, all z

  3. (i)λ 1 = 1 1, 3


(ii)λ 1 = 111 :y 1 = 1 −x,λ 1 = 131 :y 1 = 1 x, all x



  1. (i)


(ii)λ 1 = 131 :x 1 = 1 −z,y 1 = 1 0, all z



  1. (i)λ 1 = 10 (double), 8


(ii)λ 1 = 101 :x 1 = 13 z 1 − 12 y, all y and z


λ 1 = 181 : x 1 = 1 −z,y 1 = 1 − 2 z, all z






Section 17.6















  1. ψ


1

(x


1


2

(x


2


3

(x


3


4

(x


4

)


−ψ


1

(x


1


2

(x


2


3

(x


4


4

(x


3

)



1

(x


1


2

(x


3


3

(x


4


4

(x


2

)


24 6 3


0110 1


0 0 42 13 2


00 08021


320


−−



=−


10 1 1


01 1 0


00 1 0


00 0 1


1




=


322


039


0025


225



−=−






12 3


456


42 56 72


2

34 5

567

xx


xx x


xxx


026


456


789


12 3


12 20 30


7


345

678

2

234

x


xxx


xxx


xx


xxx


x






6678

89 xx


λ=± 32 :, ,xzy z z= =± 2 all


λ=±33 2,


−ψ


1

(x


1


2

(x


3


3

(x


2


4

(x


4

)



1

(x


1


2

(x


4


3

(x


2


4

(x


3

)


−ψ


1

(x


1


2

(x


4


3

(x


3


4

(x


2

)



1

(x


2


2

(x


1


3

(x


4


4

(x


3

)


−ψ


1

(x


2


2

(x


1


3

(x


3


4

(x


4

)



1

(x


2


2

(x


3


3

(x


1


4

(x


4

)


−ψ


1

(x


2


2

(x


3


3

(x


4


4

(x


1

)



1

(x


2


2

(x


4


3

(x


3


4

(x


1

)


−ψ


1

(x


2


2

(x


4


3

(x


1


4

(x


3

)



1

(x


3


2

(x


1


3

(x


2


4

(x


4

)


−ψ


1

(x


3


2

(x


1


3

(x


4


4

(x


2

)



1

(x


3


2

(x


2


3

(x


4


4

(x


1

)


−ψ


1

(x


3


2

(x


2


3

(x


1


4

(x


4

)



1

(x


3


2

(x


4


3

(x


1


4

(x


2

)


−ψ


1

(x


3


2

(x


4


3

(x


2


4

(x


1

)



1

(x


4


2

(x


1


3

(x


3


4

(x


2

)


−ψ


1

(x


4


2

(x


1


3

(x


2


4

(x


3

)



1

(x


4


2

(x


2


3

(x


1


4

(x


3

)


−ψ


1

(x


4


2

(x


2


3

(x


3


4

(x


1

)



1

(x


4


2

(x


3


3

(x


2


4

(x


1

)


−ψ


1

(x


4


2

(x


3


3

(x


1


4

(x


2

)


Chapter 18


Section 18.1



  1. (i) (ii)


(iii) 2.


Section 18.2


3.not possible 4.− 6 , 4 5. 4 , 5


6.not possible 7.










  1. 11.(0 −31)






2


5


− 2














10


− 24










30 0


02 0


00 1−















−−










542


311


10


23


34















01


10










01


− 10










01


10











1

2

1

2

1

2

1

2











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