TOÁN CAO CP 2 
 Li gii mt s bài t p trong t ài liu này dùng tham kho. Có mt s b ài 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 NH THC 
Bài 1
1)  D = 37
2)  D = 58
3)  D = 1nn
1)  D =
5)  D =
6) 
 
3 3 3 3 3 33acb bac cba c a b abc c a b  
7)  D =
 D x b x x b
 x x c x x
 
3 3 2 2 2 3 2 2abc x x bx ax cx abc x x a b c  
9)
 D x b x x x b x
 x x c x x x



 


2 3 3 2 3 2 3 2 3
2 2 2 3 3 3 2 3 2 3 2 3
a x b x c x x x x b x x a x x c x
ab ax bx x c x x x bx x x a x x c x
abc abx acx ax bcx bx cx x x x bx x x a x x c x
abc abx acx bcx
1 1
1 1
01 1
 D   c a b c a b a b
b c c a a b c a a b a b c
b c
c a
c a a b
3 1 4 3
h  D a M b M c M d M 
a b c d  
* 32M =
343
234
142
* 33M =
313
224
132
* 34M =
413
324
432
Vy: D = 8a+15b+12c-19d
2)  2 12
b  D a M b M c M d M 
c
d 
 
* 32M =
454
344
125
* 42M =
232
344
125
Vy: D = - (-2a + 8b – c - 5d) = 2a - 8b + c + 5d
3)  4 4 1
0 0 2 ( 1) 0 0
1 2 3 1 2
0 0 0
c c
2 0 0 ( 1) 0 0
3 4 5 4 5
0 0 0
c c
1)  1( 1) 2 1( 1) 3
1( 1) 4
1 1 1 1 1 1 1 1
1 1 1 1 0 2 0 0 1 ( 2) ( 2) ( 2) 8
1 1 1 1 0 0 2 0
1 1 1 1 0 0 0 2
h h h h
1( 1) 4
0 1 1 1 1 0 1 1 1 0 1 1
1 0 1 1 0 1 1 1 0 1 1 1
1 1 0 1 1 1 0 1 0 1 1 0
1 1 1 0 1 1 1 0 0 1 0 1
1 1 1 1 1
1 1 1 0 1 1
1 0 1 1 0
1 1 1 3
c c h h
1( 1) 4
2 5 1 2 1 5 2 2 1 5 2 2
3 7 1 4 1 7 3 4 0 2 1 6
3 9 2 7 2 9 3 7 0 1 1 3
4 6 1 2 1 6 4 2 0 1 2 0
2 1 6 2 1
1 1 1 3 1 1
1 2 0 1 2
3 12 6 12 3
h h c c h h
h h  D
1 4 4
3 3 5 8 1 0 0 2 1 0 0 2
3 2 4 6 3 2 4 6 0 2 4 12
2 5 7 5 2 5 7 5 0 5 7 9
4 3 5 6 4 3 5 6 0 3 5 14
2 4 12 1 2 6 1 2
1 5 7 9 1 2 5 7 9 5 7
3 5 14 3 5 14 3 5
2 98 54 150 126 45 140 2 9
h h
h h h h
1( 3) 4
0 7 1 9 1 21 3 18 21 3
0 21 3 18 15 1 15 15 1
0 15 1 15
h h h h
1 5
1( 2) 2
1( 1) 3
1 0 1 1 2 1 0 1 1 2 1 1 2 1
0 1 1 2 1 0 1 1 2 1 2 0 1 1
11 2 1 0 1 0 2 0 1 1 0 2 1 4
1 0 1 0 2 0 0 2 1 4 1 2 0 3
1 1 1 1 1 0 1 2 0 3
1 1 2 1 2 3 1 2 3
0 2 3 1 1 2 1 4 2 1
0 2 1 4 1 2 4 1 2
0 1 2 4
 
0 0 5 0 0 1 3 18 6 2
0 2 0 2 0 0 2 0 2 0
1 3 18 6 2 0 0 5 0 0
4 17 9 15 2 4 17 9 15 2
19 20 24 3 5 19 20 24 3 5
1 3 18 6 2 2 0 2 0
0 2 0 2 0 0 5 0 0
10 0 5 0 0 5 63 9 6
0 5 63 9 6 37 318 117 33
0 37 318 117 33
h h
h h
h h
( 1) 5 5 5 9 6 5 9
37 117 33 37 117
5 594 444 1404 330 5 36 180
 M 
1( 1) 2 2( 1) 3 3 4
1 2 1 4 10 1 2 1 4 10 5 1 1 7
1 3 2 5 3 0 5 1 1 7 5 3 7 9
10 5 3 7 9 0 5 3 7 9 0 2 3 7
0 0 2 3 7 0 0 2 3 7 0 0 3 15
0 0 0 3 15 0 0 0 3 15
5 1 1 7 5 1 1 7
0 2 6 16 0 2 6 16
0 2 3 7 0 0 3 9
0 0 3 15 0 0 3 15
h h
 D  



 
1( 1) 4
1( 7) 2
1(2) 4
7 3 2 6 7 3 2 6 1 12 2 3
8 9 4 9 1 12 2 3 7 3 2 6
7 2 7 3 0 5 5 3 0 5 5 3
5 3 3 4 2 6 1 2 2 6 1 2
1 12 2 3 87 12 15
0 87 12 15 1 5 5 3
0 5 5 3
0 30 5 4
h h
h h
h h
3 5 5 3 5 5
30 5 4 30 5 4 30 5




 
 
Gii h phng tr ình bng phng pháp Kramer: 
1)
* Dx2 =
150
271
112  
* Dx3 =
550
741
102  
 
* Dx2 =
213
5130
361
* Dx3 =
103
1340
611
 
1( 2) 3
1( 1) 4
1 4 1 0 1 4 1 0 2 3 5 2 3
0 2 3 5 0 2 3 5 1 8 1 0 8 1
2 0 1 0 0 8 1 0 6 1 3 6 1
1 2 0 3 0 6 1 3
6 40 30 72 76
h h
h1 1 h3
2 4 1 0 1 4 2 0 1 4 2 0
8 2 3 5 3 2 8 5 0 10 14 5
5 0 1 0 1 0 5 0 0 4 3 0
0 2 0 3 0 2 0 3 0 2 0 3
10 14 5 10 14
1 4 3 0 4 3
2 0 3 2 0
90 30 168 228
h1 2 h3
h1 1 h4
1 2 1 0 1 2 1 0 8 3 5 8 3
0 8 3 5 0 8 3 5 1 1 1 0 1 1
2 5 1 0 0 1 1 0 2 1 3 2 1
1 0 0 3 0 2 1 3
24 5 10 9 0
 x D
h1 2 h3
h1 1 h4
1 4 2 0 1 4 2 0 2 8 5 2 8
0 2 8 5 0 2 8 5 1 8 1 0 8 1
2 0 5 0 0 8 1 0 6 2 3 6 2
1 2 0 3 0 6 2 3
6 80 30 192 76
 x D
h1 2 h3
h1 1 h4
1 4 1 2 1 4 1 2 2 3 8 2 3
0 2 3 8 0 2 3 8 1 8 1 1 8 1
2 0 1 5 0 8 1 1 6 1 2 6 1
1 2 0 0 0 6 1 2
4 18 64 48 2 48 76
 x  D
1 1
2 2
3 3
4 4
228 3
1( 2) 2
1 0 3 1 1 0 3 1 1 6 3
2 1 0 1 0 1 6 3   1 2 5 2
0 2 5 2 0 2 5 2 3 0 1
0 3 0 1 0 3 0 1
5 36 – 45 12 2
h h
h1 h4
2 0 3 1 1 0 3 2 1 0 3 2
0 1 0 1 1 1 0 0 0 1 3 2
5 2 5 2 2 2 5 5 0 2 1 1
4 3 0 1 1 3 0 4 0 3 3 6
1 3 2
1 2 1 1 6 9 12 6 3 36 0
3 3 6
2
1 2 3 1 1 2 3 1 4 6 3
2 0 0 1 0 4 6 3 1( 2) 2 1 5 5 2
0 5 5 2 0 5 5 2 4 0 1
0 4 0 1 0 4 0 1
20 48 – 60 30 2
 x D h h
1( 2) 2
1 0 2 1 1 0 2 1 1 4 3
2 1 0 1 0 1 4 3 1 2 5 2
0 2 5 2 0 2 5 2 3 4 1
0 3 4 1 0 3 4 1
5 – 24 – 24 45 8 – 8 2
h h
 x  D
1( 2) 2
1 0 3 2 1 0 3 2 1 6 4
2 1 0 0 0 1 6 4 1 2 5 5
0 2 5 5 0 2 5 5 3 0 4
0 3 0 4 0 3 0 4
 20 90 60 48 2
h h
 x  D