The Chemistry Maths Book, Second Edition

(Grace) #1

Solutions to exercises 647


Section 18.3









  1. 16.not possible

  2. 18.(2 2 −1)








21.not possible 22.










25.not possible 26.













  1. 31.− 17


32.− 17 33.


34.not possible 35.(−10 2)


















  1. (i)[I




x

,I


y

] 1 = 1 iAI


z

,[I


y

,I


z

] 1 = 1 iAI


x

,[I


z

,I


x

] 1 = 1 iAI


y

(ii) 2 A


2

1







  1. 45.d


42


21












−−










22 cd


cd


BC=










=












10


01


1000


0100


0010


0001


,

















11


11


00


00










01


01


10


10



















,






















54


41


54


41


,


01


−10 7










062


0155


062

















000


6156


252


−−
























7


9


36


04











32


04











900


040


001





























522


412


28


61420


2716


258



−−


−−
























43


22 9


216


638


−−











36


012











2


2


− 1














−−


−−










137


264


137


264












111


204


−−










Section 18.4










49.singular 50.






53.both


Section 18.5



  1. (i)


(ii)



  1. (i)


(ii)


(iii) (iv)


(v) (vi)










−−− −










1122


2332


1


5


0112


57 8 6


−−

























100


010


001


100


010


001




























100


010


001


10 0


01 0


00 1−














cos sin


sin cos


θθ


θθ


0


010


− 0














10 0


0


0


cos sin


sin cos


θθ


θθ















1

2

1

2

1

2

1

2

0


0


001

















xx y


yx y


zz


′= −


′= +


′=









cos sin


sin cos


θθ


θθ


1


4


50 22


43 19












1


2


2400


1300


0021


0043




















1

2

1

2

1

2

1

2

0


010


− 0
















1


6


111


4108


175



−−















1


14


13


− 42









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