Preview:
DESCRIPTION
Bai Tap Ma Tran
Citation preview
TOÁN CAO CP 2
Li gii mt s bài t p trong t ài liu này dùng tham
kho. Có mt s bài t p do mt s
sinh viên gii. Khi hc, sinh viên cn la chn nhng phng pháp phù hp và
n gin
hn. Chúc anh ch em sinh viên hc tp t t
BÀI TP V
Bài 1:
1)
2( 2) 3
1 2 1( 2) 2 3
7 2 3 15 2 5 1 0 2 5 1 0
5 3 2 15 5 3 2 15 1 13 0 15
10 11 5 36 0 5 1 6 0 5 1 6
1 13 0 15 1 13 0 15
2 5 1 0 0 31 1 30
0 5 1 6 0 5 1 6
h h h h
A B
H phng tr ình ã cho tng ng vi h phng tr ình:
1 2 1
2 3 2
1( 1) 2 1( 2) 3 1 2
1( 2) 2 1( 1) 2 2 3
2 1 210 2 1 2 10 1 1 4 9
3 2 2 1 1 1 4 9 2 1 2 10
5 4 3 4 1 2 7 16 1 2 7 16
1 1 4 9 1 1 4 9
0 1 10 28 0 1 10 28
0 1 3 7 0 0 7 21
h h h h h h
h h h h h h
A B
H phng tr ình ã cho tng ng vi h phng tr ình:
1 2 3 1
1( 3) 3
1 2 1 3 1 2 1 3 1 2 1 3
2 5 4 5 0 1 2 1 0 1 2 1
3 4 2 12 0 2 5 3 0 0 1 1
h h h h
h h A B
H phng tr ình ã cho tng ng vi h phng tr ình:
1 2 3 1
3( 2) 2 1(3) 3
2( 2) 3 2 3
2 1 3 1 1 2 1 6 1 2 1 6
5 2 6 5 1 4 2 9 0 2 1 3
3 1 4 7 3 1 4 7 0 5 1 11
1 2 1 6 1 2 1 6
0 2 1 3 0 1 3 5
0 1 3 5 0 2 1 3
h h h h
h h h h
h h h h
H phng tr ình ã cho tng ng vi h phng tr ình:
1 2 3 1
2( 2) 3 1( 1) 3
2 3
2 1 2 8 1 1 2 7 1 1 2 7
3 2 4 15 3 2 4 15 0 1 2 6
5 4 1 1 1 0 7 29 0 1 5 22
1 1 2 7
0 1 2 6
0 0 7 28
h h h h
h h h h
H phng tr ình ã cho tng ng vi h phng tr ình:
1 2 3 1
1( 3) 3
1 2 3 1 1 2 3 1 1 2 3 1
2 5 8 4 0 1 2 2 0 1 2 2
3 8 13 7 0 2 4 4 0 0 0 0
h h h h
h h A B
2 2 2 2 2 2
ý
x x x t t R x x
x t x
1)
x x x x
x x x x
x x x x
x x x x
2 2 1 1 4 2 2 1 1 4
4 3 1 2 6 0 1 1 0 2
8 5 3 4 12 0 3 1 0 4
3 3 2 2 6 0 0 1/ 2 1/ 2 0
2 2 1 1 4 2 2 1 1 4
0 1 1 0 2 0 1 1 0 2
0 0 2 0 2 0
0 0 1/ 2 1/ 2 0
A B
Th 4 1 x vào (3) 3 1 x
1 x
Th x3, x2, x4 vào (1) ta c: 1 1 x
Vy nghim ca phng tr ình ã cho là:
1
2
3
4
1
1
1
1
x
x
x
x
2)
5 2 1
2 3 11 5 2 1 1 5 2 1
1 1 5 2 1 2 3 11 5 2 /
2 1 3 2 3 2 1 3 2 3
1 1 3 4 3 1 1 3 4 3
A B
h3(-3) h4
1 1 5 2 1 1 1 5 2 1 1 1 5 2 1
0 1 1 1 0 0 1 1 1 0 0 1 1 1 0
0 1 7 2 5 0 0 6 1 5 0 0 2 2 4
0 0 2 2 4 0 0 2 2 4 0 0 6 1 5
1 1 5 2 1
0 1 1 1 0
0 0 2 2 4
0 0 0 7 7
1 x
Th x3, x4 vào (2) ta c: 2 0 x
Th x3, x2, x4 vào (1) ta c: 1 2 x
Vy nghim ca phng tr ình ã cho là:
3)
9 4 7 2
x x x x
x x x x
x x x x
2 7 3 1 6 1 2 1 1 2
/ 3 5 2 2 4 3 5 2 2 4
9 4 1 7 2 9 4 1 7 2
A B
2 2 (1)
x x x x
x x x
x s
7 4 3 5
x x x x
x x x x
x x x x
3 5 2 4 2 3 5 2 4 2
/ 7 4 1 3 5 1 6 3 5 1
5 7 4 6 3 5 7 4 6 3
1 6 3 5 1 1 6 3 5 1
3 5 2 4 2 0 23 11 19 1
5 7 4 6 3 0 23 11 19 2
1 6 3 5 1
0 23 11 19 1
h h
x x x x
1 3 1( 2) 2
2 1 1 1 1 0 0 1 2 1
2 1 0 3 2 2 1 0 3 2
3 0 1 1 3 1 1 1 4 5
3 2 2 5 6 0 3 2 8 8
1 1 1 4 5 1 1 1 4
2 1 0 3 2 0 3 2 11
0 0 1 2 1 0 0 1 2
0 3 2 8 8 0 3
h h h h h h
h h h h
h h
H ph ng trình ã cho t ng ng v i h ph ng
trình:
1
2 3 4
3 3 4
0 4 5 2
3 2 11 12 5 45 0, 2, , 2 1 3 33
4 3 4
x x
x x
1( 4) 4
2( 7) 4
1 2 3 4 11 1 2 3 4 11
2 3 4 1 12 0 1 2 7 10
3 4 1 2 13 0 2 8 10 20
4 1 2 3 14 0 7 10 13 30
1 2 3 4 11
0 1 2 7 10
0 0 4 4 0
0 0 4 36 40
h h h h
2 3 4 2
1 4 4 0
x x x
2(7) 4
1 2 3 4 4 1 2 3 4 4
0 1 1 1 3 0 1 1 1 3
1 3 0 3 1 0 5 3 1 3
0 7 3 1 3 0 7 3 1 3
1 2 3 4 4 1 2 3 4 4
0 1 1 1 3 0 1 1 1
0 0 2 4 12 0 0 2 4
0 0 4 8 24 0 0 0 0
h h
3 3 3
x x x x x x
x x x t x x x t R
x x x t x x
x x t
x x x x
x x x x
x x x x
1( 3) 3
3 4 1 2 3 3 4 1 2 3 3 4 1 2 3
6 8 2 5 7 0 0 0 1 1 0 0 0 1 1
9 12 3 10 13 0 0 0 4 4 0 0 0 0 0
h h h h
h h A B
4
34
3 4 2 3 1 ,
1
1
x x x x x t x t s R
x s x x
1 2 3 4
1 2 3 4
3 3 14 8
x x x x
x x x x
x x x x
1( 3) 3
4
9 3 5 6 4 3 1 3 14 8 3 1 3 14 8
6 2 3 4 5 6 2 3 4 5 0 0 3 24 21
3 1 3 14 8 9 3 5 6 4 0 0 4 36 28
3 1 3 14 8 3 1 3
0 0 1 8 7
0 0 1 9 7
h h h h
8 7
x t x x t R
x x x
1( 1) 4 3( 1) 4
3 2 5 1 3 1 2 0 4 3
2 3 1 5 3 2 3 1 5 3
1 2 0 4 3 3 2 5 1 3
1 1 4 9 22 1 1 4 9 22
1 2 0 4 3 1
0 7 1 13 3
0 8 5 13 12
0 3 4 13 25
h h
h h h h
1 2 0 4 3 1 2 0 4 3
0 1 6 0 9 0 1 6 0 9
0 0 43 13 60 0 0 1 0 2
0 0 29 0 58 0 0 43 13 60
h h h h
h h
H ph ng trình ã cho t ng ng v i
h ph ng trình:
1 2 4 1
3 2 3 7
x x x x
x x x x
x x x x
x x x mx
1( 3) 4
1 1 6 4 6 1 1 6 4 6
3 1 6 4 2 0 4 12 8 16
2 3 9 2 6 0 1 21 10 6
3 2 3 8 7 0 1 21 20 25
1 1 6 4 6
0 1 3 2 4
0 1 21 10 6
0 1 21 20 25
h h h h
1 1 6 4 6 1 1 6 4 6
0 1 3 2 4 0 1 3 2 4
0 0 6 6 7 0 0 6 6 7
0 0 12 6 5 0 0 0 6 9
h h h h
H ph ng trình ã cho t ng ng v i
h ph ng trình:
1
2 3 4
3 3 4
36 9
x x x x
x x x x
1( 1) 4
2 21 3
2 1 1 1 1 2 1 1 1 1
2 1 0 3 2 0 0 1 2 1
3 0 1 1 3 1 1 2 2 4
2 2 2 5 6 0 3 3 6 7
1 1 2 2 4 1 1 2 2
0 0 1 2 1 0 0 1 2
2 1 1 1 1 0 3 5 5
0 3 3 6 7 0
h h h h
1 1 2 2 4 1 1 2 2 4
0 0 1 2 1 0 3 5 5 9
0 3 5 5 9 0 0 1 2 1
0 0 2 1 2 0 0 2 1 2
1 1 2 2 4
0 3 5 5 9
0 0 1 2 1
0 0 0 3 4
h h h h
H ph ng trình ã cho t ng ng v i
h ph ng trình:
1
2 3 4
3 3 4
3 5 5 9 5 2 1 3
43 4
x x x x
7 8 5 40
x x x x
x x x x
x x x x
x x x x
1( 2) 4
1( 3) 3
3 5 3 2 12 3 5 3 2 12
4 2 5 3 27 1 7 8 1 15
7 8 1 5 40 1 2 5 1 16
6 4 5 3 41 0 6 11 117
1 2 5 1 16 1 2 5
1 7 8 1 15
3 5 3 2 12
0 6 11 117
h h h h
1 2 5 1 16 1 2 5 1 16
0 5 3 0 1 0 1 8 1 18
0 1 12 1 38 0 1 12 1 38
0 1 8 1 18 0 5 3 0 1
1 2 5 1
0 1 8 1
16 1 2 5 1 16
18 0 1 8 1 18
4 2 20 0 0 2 1 10
0 0 37 5 91 0 0 37 5 91
1 2 5 1 16 1 2 5 1 16
0 1 8 1 18 0 1 8 1 18
0 0 2 1 10 0 0 1 23 89
0 0 1 23 89 0 0 2 1 10
h
h
2 3 4 2
x x x x
2 3 10
1( 4) 3
4 4 5 5 0 1 1 5 0 10
2 0 3 1 10 2 0 3 1 10
1 1 5 0 10 4 4 5 5 0
0 3 2 0 1 0 3 2 0 1
1 1 5 0 10 1 1 5 0 10
0 2 13 1 30 0 1 15 1 31
0 0 25 5 40 0 0 25 5 40
0 3 2 0 1 0 3 2 0 1
h h
1 1 5 0 10 1 1 5 0 10
0 1 15 1 31 0 1 15 1 31
0 0 25 5 40 0 0 5 1 8
0 0 43 3 92 0 0 43 3 92
1 1 5 0 10 1
0 1 15 1 31
0 0 5 1 8
0 0 2 12 20
h h h
h h
H ph ng trình ã cho t ng ng v i
h ph ng trình:
1 2 3 1
2 3 4 2
3 2 6
3 3 6
2( 1) 4
2 1 3 2 4 1 4 0 0 2
3 3 3 2 6 3 3 3 2 6
3 1 1 2 6 0 4 4 4 0
3 1 3 1 6 0 4 0 3 0
h h h h
h h A B
1 4 0 0 2 1 4 0 0 2
0 9 3 2 0 0 1 1 1 0
0 4 4 4 0 0 9 3 2 0
0 0 4 1 0 0 0 4 1 0
1 4 0 0 2 1 4 0 0
0 1 1 1 0 0 1 1 1
0 0 12 11 0 0 0 4 1
0 0 4 1 0 0 0 12
h h h h
h h
1( 1) 4
1 1 2 3 1 1 1 2 3 1
3 1 1 2 4 0 4 7 11 7
2 3 1 1 6 0 1 5 7 8
1 2 3 1 4 0 1 1 4 5
1 1 2 3 1 1 1 2
0 1 5 7 8
0 4 7 11 7
0 1 1 4 5
h h h h
1 1 2 3 1 1 1 2 3 1
0 1 5 7 8 0 1 5 7 8
0 0 9 13 13 0 0 1 8 8
0 0 2 1 1 0 0 2 1 1
h h h
h h
2 3 4 2
x x x x
1( 4) 4
3( 1) 3 2
1 2 3 4 5 1 2 3 4 5
2 1 2 3 1 0 3 4 5 9
3 2 1 2 1 0 4 8 10 14
4 3 2 1 5 0 5 10 15 25
1 2 3 4 5
0 1 4 5 5
0 4 8 10 14
0 1 2 5 11
h h h h
h
1 2 3 4 5 1 2 3 4 5
0 1 4 5 5 0 1 4 5 5
0 0 2 0 6 0 0 2 0 6
0 0 8 10 6 0 0 0 10 30
h h h h
H ph ng trình ã cho t ng ng v i
h ph ng trình:
1 2 3 4 1
2 3 4 2
4 5 5 2
x x x x
2 7 2
1( 1) 4
3( 1) 4
1 1 1 1 2 1 1 1 1 2 1 1 1 1 2
1 2 3 4 2 0 1 2 3 0 0 1 2 3 0
2 3 5 9 2 0 1 3 7 2 0 0 1 4 2
1 1 2 7 2 0 0 1 6 0 0 0 1 6 0
1 1 1 1 2
0 1 2 3 0
0 0 1 4 2
0 0 0 2 2
h h h h h h
h h
h h
A B
H ph ng trình ã cho t ng ng v i
h ph ng trình:
1 2 3 4 1
2 3 4 2
x x x x
Bài 3:
Gii các h phng tr ình tuyn tính thun nht sau:
1)
h2 h3 49
- 28
2 1 4 0 1 11 5 0 1 11 11 0
/ 3 5 7 0 3 5 7 0 0 28 8 0
4 5 6 0 4 5 6 0 0 49 14 0
1 11 11 0
0 28 8 0
0 0 0 0
Th x3 vào (1), ta c: 1 2 2 2
28 55 11 11
3 2 7
3 5 2 0 1 1 4 0 1 1 4 0
4 7 5 0 4 7 5 0 0 3 21 01 3/ 1 1 4 0 3 5 2 0 0 2 14 0
2 9 6 0 2 9 6 0 0 7 14 0
1 1 4 0
0 1 7 0
0 1 7 0
0 1 2 0
h h h h
h h A B
1 1 4 0 1 1 4 0
0 1 7 0 0 1 7 0
0 0 0 0 0 0 5 0
0 0 5 0 0 0 0 0
h
3
x
2 5 0
1( 1) 3
2 1 3 7 0 2 1 3 7 0 2 1 3 7 0
4 2 7 5 0 0 0 1 9 0 0 0 1 9 0
2 1 1 5 0 0 0 2 12 0 0 0 0 6 0
h h h h
h h A B
H
0 2 9 0
x x t x x t R
x x x
x x x x
x x x x
x x x x
x x x x
1 2 4 3 0 1 2 4 3 0
3 5 6 4 0 0 1 6 5 0
4 5 2 3 0 0 3 18 15 0
3 8 24 19 0 0 2 12 10 0
1 2 4 3 0
0 1 6 5 0
0 0 0 0 0
0 0 0 0 0
h h h h
2 3 4
32 3 4
6 5 0
x t s x x x
x x x x x t s x x x t s R
x t x x x x
x s