646 Solutions to exercises
- 6 8.− 4 9. 30
- (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
- (ii)x 1 = 1 (z 1 + 1 3) 25 ,y 1 = 1 (7z 1 − 1 4) 2 5, all z
- (ii)x 1 = 1 z 2 3,y 1 = 1 − 2 z 2 3, all z
- (i)λ 1 = 1 1, 3
(ii)λ 1 = 111 :y 1 = 1 −x,λ 1 = 131 :y 1 = 1 x, all x
- (i)
(ii)λ 1 = 131 :x 1 = 1 −z,y 1 = 1 0, all z
- (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
- ψ
1
(x
1
)ψ
2
(x
2
)ψ
3
(x
3
)ψ
4
(x
4
)
−ψ
1
(x
1
)ψ
2
(x
2
)ψ
3
(x
4
)ψ
4
(x
3
)
+ψ
1
(x
1
)ψ
2
(x
3
)ψ
3
(x
4
)ψ
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
)ψ
2
(x
3
)ψ
3
(x
2
)ψ
4
(x
4
)
+ψ
1
(x
1
)ψ
2
(x
4
)ψ
3
(x
2
)ψ
4
(x
3
)
−ψ
1
(x
1
)ψ
2
(x
4
)ψ
3
(x
3
)ψ
4
(x
2
)
+ψ
1
(x
2
)ψ
2
(x
1
)ψ
3
(x
4
)ψ
4
(x
3
)
−ψ
1
(x
2
)ψ
2
(x
1
)ψ
3
(x
3
)ψ
4
(x
4
)
+ψ
1
(x
2
)ψ
2
(x
3
)ψ
3
(x
1
)ψ
4
(x
4
)
−ψ
1
(x
2
)ψ
2
(x
3
)ψ
3
(x
4
)ψ
4
(x
1
)
+ψ
1
(x
2
)ψ
2
(x
4
)ψ
3
(x
3
)ψ
4
(x
1
)
−ψ
1
(x
2
)ψ
2
(x
4
)ψ
3
(x
1
)ψ
4
(x
3
)
+ψ
1
(x
3
)ψ
2
(x
1
)ψ
3
(x
2
)ψ
4
(x
4
)
−ψ
1
(x
3
)ψ
2
(x
1
)ψ
3
(x
4
)ψ
4
(x
2
)
+ψ
1
(x
3
)ψ
2
(x
2
)ψ
3
(x
4
)ψ
4
(x
1
)
−ψ
1
(x
3
)ψ
2
(x
2
)ψ
3
(x
1
)ψ
4
(x
4
)
+ψ
1
(x
3
)ψ
2
(x
4
)ψ
3
(x
1
)ψ
4
(x
2
)
−ψ
1
(x
3
)ψ
2
(x
4
)ψ
3
(x
2
)ψ
4
(x
1
)
+ψ
1
(x
4
)ψ
2
(x
1
)ψ
3
(x
3
)ψ
4
(x
2
)
−ψ
1
(x
4
)ψ
2
(x
1
)ψ
3
(x
2
)ψ
4
(x
3
)
+ψ
1
(x
4
)ψ
2
(x
2
)ψ
3
(x
1
)ψ
4
(x
3
)
−ψ
1
(x
4
)ψ
2
(x
2
)ψ
3
(x
3
)ψ
4
(x
1
)
+ψ
1
(x
4
)ψ
2
(x
3
)ψ
3
(x
2
)ψ
4
(x
1
)
−ψ
1
(x
4
)ψ
2
(x
3
)ψ
3
(x
1
)ψ
4
(x
2
)
Chapter 18
Section 18.1
- (i) (ii)
(iii) 2.
Section 18.2
3.not possible 4.− 6 , 4 5. 4 , 5
6.not possible 7.
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
−