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Гродненский государственный университет им. Я. Купалы

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<<< < Предыдущая 1 2 3 4 56 / 186 7 8 9 10 11 12 13 14 15 16 17 18 > Следующая >>>

2x − x = 0
	1	2
14 1x1 + 2x2 − x3 = 1
	+ x3	= 0
x2

1 2 3 = 7

16.2x1 − 3x2 + 2x3 = 9

x1 + 2x2 + 3x3 = 15x + 8x − x

1 2 3 = 12

21.x1 − 4x2 + 3x3 = −22

3x1 − x2 − 2x3 = 02x + 3x + 5x

1 2 3 = 12

23.x1 + 2x2 + x3 = 7x2 − x3 = −14x + 2x − x

2x + x − x = 0

1 2 3

25.3x2 − 4x3 = −6

x1 + x3 = 1

2x − 3x − x = −6

1 2 3

27.3x1 + 4x2 + 3x3 = −5

x1 + x2 + x3 = −2

3x − 3x + 2x = 2

1 2 3

29.4x1 − 5x2 + x3 = 2

x1 − 2x2 = 5

1 2 3 = 9

31.3x1 − 5x2 + x3 = −4

4x1 − 7 x2 + x3 = 52x − x + 3x

x + x − x = 6

1 2 3

18.2x1 + 3x2 − 4x3 = 217x1 − x2 − 3x3 = 6

2x − 3x + 5x = 1

1 2 3

20.3x1 − x2 + 5x3 = 10

x1 + 2x2 − 4x3 = −7

1 + 5x2 − x3 = 3

33.2x1 + 4x2 − 3x3 = 2

3x1 − x2 − 3x3 = 7x

2x + x			= 3
	1	2
22. x1	+ x3 = 1
		+ x2	+ 2x3 = 0
3x1

1 2 3 = 4

24.x1 + 2x2 + 2x3 = 53x1 + x2 − 5x3 = 22x + 3x − x

	x + 2x		+ x = 8
	1	2	3
26.	−2x1 + 3x2 − 3x3 = −5

	3x1 − 4x2 + 5x3 = 10
	2x − x		= 0
		1 2
28.	x1	+ 2x2 − x3 = −2
		+ x3 = −5
	x2	+ x3 = −5

1 2 3 = 1

30.2x1 + 2x2 − 3x3 = 9

x1 − x2 + x3 = 23x + x + 2x

2x − 3x + x = 2

1 2 3

32.3x1 + 2x2 − 3x3 = 15x1 − 2x2 − 2x3 = 4

2x − 3x − x = −6

1 2 3

35.3x1 + 4x2 + 3x3 = −5

x1 + x2 + x3 = −2

2x − 3x + 2x = 2

1 2 3

36.x1 + 2x2 − x3 = 23x1 + x2 + x3 = 8

2x − 3x + 5x = 11

1 2 3

37.3x1 − x2 + 5x3 = 16

x1 + 2x2 − 4x3 = −7

x	+ x	+	3x	= 5
1	2		3
39. x1	+ x2	+	3x3	= 5
			− x3 = 4
2x1 + 3x2			− x3 = 4

5x + 8x − x = 7

1 2 3

41.2x1 − 3x2 + 2x3 = 9

x1 + 2x2 + 3x3 = 1

x + 5x + 2x = 5

1 2 3

43.2x1 + 3x2 + 4x3 = 33x1 + 4x2 + 2x3 = 8

5x + 2x + 13x = 2

1 2 3

45.3x1 − x2 + 5x3 = 02x1 − x2 + 5x3 = 4

2x + x			− x	= 0
	1	2	3
34 3x2 − 4x3 = −6
	+ x3	= 1
x1	+ x3	= 1
x − 2x			− x	= 5

1 2 3

47.3x1 + 4x2 − 2x3 = 13

x2 + 3x3 = −6

2x − 3x + 2x = 2

1 2 3

49.3x1 + x2 + x3 = 8x1 + 2x2 − x3 = 2

2x + 3x − x = 4

1 2 3

51.3x1 + x2 − 4x3 = 0

x1 + 2x2 + 3x3 = 6

3x + 6x + 2x = 4

1 2 3

38.4x1 − x2 − 3x3 = 12x1 + 4x2 + x3 = 4

2x + x − x = 0

1 2 3

40.3x1 − 2x2 + 4x3 = −15

x1 − x2 − 3x3 = 13

	x	− x	= −3
	2	3
42.	4x1 + 2x2 − x3 = 0
		+ 2x2 + x3 = 1
	x1	+ 2x2 + x3 = 1
	x	+ 2x		+ x		= 1
	1		2		3
44	x2	− x3	= −3
		− x2 − x3 = 0
	x1	− x2 − x3 = 0

x + 5x + x = 0

1 2 3

46.2x1 − 4x2 − 3x3 = −13x1 + 4x2 + 2x3 = 8

	x + 2x			+ x		= 8
		1	2	3
48.	x2 − x3 = −3
			+ 2x2 − x3 = 0
	4x1		+ 2x2 − x3 = 0
	1x + 2x			− x		= 1
		1	2		3

50.	x2 + x3 = 0
			− x2	= 0
	2x1		− x2	= 0

x − 4x + 3x = −22

1 2 3

55.3x1 − x2 − 2x3 = 02x1 + 3x2 + 5x3 = 12

	x + 2x + x = 7
	1		2	3
57.	x2 − x3 = −1
			+ 2x2 − x3 = 12
	4x1		+ 2x2 − x3 = 12
	3x		− 4x	= −6
		2	3
59.	x1	+ x3 = 1
			+ x2 − x3 = 0
	2x1		+ x2 − x3 = 0
	3x + 4x + 3x = −5
		1	2	3
61.	x1	+ x2 + x3 = −2
			− 3x2 − x3 = −6
	2x1		− 3x2 − x3 = −6
	4x − 5x			+ x = 2

1 2 3

63.x1 − 2x2 = 5

3x1 − 3x2 + 2x3 = 2

2x − 3x + 2x = 9

1 2 3

52.x1 + 2x2 + 3x3 = 1

5x1 + 8x2 − x3 = 7

2x + 3x − 4x = 21

1 2 3

53.7x1 − x2 − 3x3 = 6

x1 + x2 − x3 = 6

3x − x			+ 5x = 10
	1	2	3
54 x1	+ 2x2 − 4x3 = −7
		− 3x2 + 5x3 = 1
2x1

3x − 5x + x = −4

1 2 3

65.4x1 − 7 x2 + x3 = 52x1 − x2 + 3x3 = 9

2x + x			= 3
	1	2
67. x1	+ x3 = 1
		+ x2	+ 2x3 = 0
3x1
x + 5x			− x = 3

1 2 3

56.2x1 + 4x2 − 3x3 = 23x1 − x2 − 3x3 = 7

x + 2x + 2x = 5

1 2 3

58.3x1 + x2 − 5x3 = 22x1 + 3x2 − x3 = 4

−2x1 + 3x2 − 3x3 = −5

60. 3x1 − 4x2 + 5x3 = 10

x1 + 2x2 + x3 = 8

	x + 2x			− x	= −2
		1	2	3
			+ x3 = −5
62.	x2		+ x3 = −5
				= 0
	2x1 − x2			= 0
	2x + 2x − 3x = 9
			1	2	3
64	x1		− x2 + x3 = 2
				+ 2x3 = 1
	3x1 + x2			+ 2x3 = 1

3x + 2x − 3x = 1

1 2 3

66.5x1 − 2x2 − 2x3 = 42x1 − 3x2 + x3 = 2

2x + x − x = 0

1 2 3

68.3x2 − 4x3 = −6

x1 + x3 = 1

1 2 3 = 2

69.4x1 − 5x2 + x3 = 2

x1 − 2x2 = 53x − 3x + 2x

x − x − x = 0

1 2 3

71.x1 + 2x2 + x3 = 1

x2 − x3 = −3

2x − 3x − x = −6

	1	2	3
73. x1	+ x2 + x3		= −2
		+ 4x2 + 3x3 = −5
3x1		+ 4x2 + 3x3 = −5

2x − 3x + 2x = 2

1 2 3

75.3x1 + x2 + x3 = 8x1 + 2x2 − x3 = 2

2x − 3x + 5x = 11

1 2 3

77.x1 + 2x2 − 4x3 = −7

3x1 − x2 + 5x3 = 16

	x + x + 3x = 5
	1		2	3
79.	x1 + x2 + 3x3 = 5
			+ 3x2	− x3 = 4
	2x1		+ 3x2	− x3 = 4
	5x + 8x			− x = 7
		1	2	3
81.	x1	+ 2x2 + 3x3 = 1
			− 3x2	+ 2x3 = 9
	2x1		− 3x2	+ 2x3 = 9

x + 5x + 2x = 5

1 2 3

83.3x1 + 4x2 + 2x3 = 82x1 + 3x2 + 4x3 = 3

2x − x + 5x = 4

1 2 3

70.5x1 + 2x2 + 13x3 = 23x1 − x2 + 5x3 = 0

	x	+ 3x	= −6
	2	3
72.	x1 − 2x2 − x3 = 5

	3x1 + 4x2 − 2x3 = 13
	2x − 3x + 2x = 2
		1	2	3
74	x1	+ 2x2 − x3 = 2
			+ x3 = 8
	3x1 + x2		+ x3 = 8
	x + 2x		+ 3x	= 6

1 2 3

76.2x1 + 3x2 − x3 = 43x1 + x2 − 4x3 = 0

3x + 6x + 2x = 4

1 2 3

78.2x1 + 4x2 + x3 = 44x1 − x2 − 3x3 = 1

	2x + x			− x	= 0
		1	2	3
80.	x1	− x2 − 3x3 = 13

	3x1 − 2x2 + 4x3 = −15
	x	− x	= −3
	2	3
82.	x1 + 2x2 + x3 = 1

	4x1 + 2x2 − x3 = 0
	x + 2x			+ x	= 1
	1		2	3
84	x1 − x2 − x3 = 0
		− x3 = −3
	x2	− x3 = −3
	2x − 4x − 3x = −1
		1		2	3
85.	x1	+ 5x2 + x3			= 0

	3x1 + 4x2 + 2x3 = 8

2x + 3x + 5x = 12

1 2 3

91.x1 − 4x2 + 3x3 = −22

3x1 − x2 − 2x3 = 0

4x + 2x − x = 12

1 2 3

93.x1 + 2x2 + x3 = 7

x2 − x3 = −1

2x + x − x = 0

1 2 3

95.3x2 − 4x3 = −6

x1 + x3 = 1

1 2 3 = 8

87.4x1 + 2x2 − x3 = 0

x2 − x3 = −3x + 2x + x

	1x + 2x				− x	= 1
		1		2	3

89.	2x1 − x2			= 0
			+ x3 = 0
	x2		+ x3 = 0
	2x − 3x + 2x = 9
			1	2		3
86.	5x1 + 8x2 − x3 = 7
			+ 2x2	+ 3x3		= 1
	x1		+ 2x2	+ 3x3		= 1
	2x + 3x − 4x = 21
			1	2		3
88.	x1		+ x2 − x3 = 6
				− 3x3		= 6
	7x1 − x2			− 3x3		= 6
	2x − 3x + 5x = 1
			1	2		3
90… 3x1 − x2 + 5x3						= 10
			+ 2x2	− 4x3		= −7
	x1		+ 2x2	− 4x3		= −7

2x − 3x − x = −6

1 2 3

92.3x1 + 4x2 + 3x3 = −5

x1 + x2 + x3 = −2

3x − 3x + 2x = 2
	1	2	3
94 4x1 − 5x2 + x3 = 2
	− 2x2	= 5
x1

1 2 3 = 9

96.3x1 − 5x2 + x3 = −4

4x1 − 7 x2 + x3 = 52x − x + 3x

	2x + 4x − 3x = 2						−2x + 3x − 3x = −5
		1		2	3			1	2	3
97.	x1	+ 5x2 − x3 = 3				98.	x1 + 2x2 + x3 = 8
			− x2	− 3x3 = 7				− 4x2	+ 5x3 = 10
	3x1		− x2	− 3x3 = 7			3x1	− 4x2	+ 5x3 = 10
	x + x = 1						x + 2x − x = −2
	1		3				1	2	3
99.	2x1 + x2			= 3		100.	2x1 − x2		= 0
			+ x2	+ 2x3 = 0				+ x3 = −5
	3x1		+ x2	+ 2x3 = 0			x2	+ x3 = −5

Задача 5. Исследовать систему на совместность методом Гаусса, если система совместна, то найти ее решение.

x + 2x

+ 3x

− x

= 1

x1 + x2 − 3x4 − x5 = 0

3x1 + 2x2 + x3 − x4 + x5 = 1

x1 − x2 + 2x3 − x4 = 0

2x1 + 3x2 + x3 + x4 = 1

4x − 2x + 6x + 3x − 4x = 0

+ 2x2 + 2x3 − x4 − 2x5 = 1

2x1

2x1 + 4x2 − 2x3 + 4x4 − 7 x5 = 0

x − 2x

+ x

− x

= 0

2x + 3x

− x

+ 5x

= 0

− x

+ x

= 0

− 7 x

= 0

2x + x

3x − x

+ 2x

+ 7 x2 − 5x3 − 5x4 + 5x5 = 0

4x1 + x2 − 3x3 + 6x4 = 0

− 2x3 + x4 − x5 = 0

− 2x2

+ 4x3

− 7 x4 = 0

3x1 − x2

2x + x

− x

+ x

= 1

3x1 + 4x2 − 5x3 + 7 x4 = 0

− x2 + x3 + x4 − 2x5 = 0

− 3x

+ 3x

− 2x

= 0

+ 4x5 = 2

3x1 + 3x2 − 3x3 − 3x4

4x − 5x

− 5x

+ 7x

= 3

4x1 + 11x2 − 13x3 + 16x4 = 0

− 2x2 + x3

+ 3x4 = 0

7x1

4.
x − x				+ 2x					+ 3x						+ 4x					= 0
	1		2					3					4						5
2x1 + x2 − x3 + 2x4 = 0
		+ 2x2 + x3 + x4 + 3x5 = 0
− x1		+ 2x2 + x3 + x4 + 3x5 = 0
x + 5x					− 8x					− 5x						− 12x						= 0
	1			2					3					4							5
3x − 7 x					2	+ 8x				3	+ 8x					4	+ 13x					5	= 0
	1				2					3						4						5
	6.
x − 2x					+ x				− x				+ x					= 0
	1			2	− x			3				4					5			= 0
2x + x					− x				+ 2x						− 3x					= 0
	1			2				3					4						5
3x1 − 2x2 − x3 + x4 − 2x5 = 0
		− 5x2 + x3 − 2x4 + 2x5 = 0
2x1		− 5x2 + x3 − 2x4 + 2x5 = 0
8.
x + x				+ x				= 6
	1		2				3
4x1 + x2 + 3x3 = 15
		+ 2x2 − x3 = 4
3x1		+ 2x2 − x3 = 4
2x		− x			+ x				= 3
	1			2				3
7x		+ 5x			2	− x			3	= 14
	1				2				3
10.
x + 3x					+ 5x					− 4x						= −1
	1			2					3					4		+ x				= −1
x + 3x					+ 2x					− 2x						+ x				= −1
	1			2					3						4				5
x1 − 2x2 + x3 − x4 − x5 = 3
					+ x3 + x4 − x5 = 3
x1 − 4x2					+ x3 + x4 − x5 = 3
12.
2x + x − x + x = 1
	1		2				3				4
3x − 2x + 2x − 3x + 5x = 2
	1			2					3						4					5
5x1 + x2 − x3 + 2x4 − x5 = −1
		− x2			+ x3 − 3x4 = 4
2x1		− x2			+ x3 − 3x4 = 4

14.

3x + 2x

+ x

+ 3x

+ 5x

= 0

6x + 4x

+ 3x

+ 5x

+ 7 x

9x1 + 6x2 + 5x3 + 7 x4 + 9x5 = 0

+ 2x2

+ 4x4 + 8x5 = 0

3x1

16.

x + x

= 4

= 5

x2 + 2x4

x3 + 3x4 = 6

x + 2x

+ 3x

+ 14x

= 32

+ 5x2

+ 6x3 + 32x4 = 77

4x1

18.

x + x

+ x

= 7

= −2

3x + 2x

+ x

− 3x

x2 + 2x3 + 2x4 + 6x5 = 23

+ 4x2

+ 3x3 + 3x4 − x5 = 12

5x1

11.

x − x

+ 7 x

− 2x

= 2

= 1

2x − 3x

+ 8x

− 4x

4x1 + 2x2 + 19x3 + x4 = 8

− 5x2

+ 11x3 − 3x4 = −3

6x1

13.

x + 3x

+ x

+ 4x

= 2

= 1

2x − 3x

+ 2x

+ 8x

4x1 + 3x2 + 4x3 − 4x4 = 0

x1 + 6x2 − x3 + 12x4 = 6

x1 + x2 − x3 + x4 = 22x1 − x2 + x3 − 4x4 = 0

4x1 + x2 + x3 − 2x4 = 4

5x1 + 2x2 − x4 = 6

17.

x1 + x2 − x3 − x4 = 0x1 + 2x2 + 3x3 + 4x4 = 0

3x1 − 2x2 + x3 − 5x4 = 0

x1 − 5x2 − x3 − 8x4 = 0

19.

x2 + x3 + x4 = 3

x1 + x2 + 6x3 + 3x4 = −3

5x2 − 7x3 + 4x4 = 5

		+ 3x2 + 5x3 + 2x4 = 1
2x1		+ 3x2 + 5x3 + 2x4 = 1
20.
x	+ x			= 1
1			2
2x	2	− x3 = −1
		+ x2 − 2x3 + x4 = −5
2x1		+ x2 − 2x3 + x4 = −5

− 2x2 + x3 − 2x4 + x5 = 6
	+ x2 − 4x4 + 2x5 = 11
x1	+ x2 − 4x4 + 2x5 = 11

x1 + x2 + x3 = 0

− x2 4 = 0

22.2x1 + 2x2 + x5 = 0

2x1 − 2x2 + x6 = 0x1 + x

+ x2 − x3 − x5 = 1

24.

3x + 2x

− x

+ 3x

+ 5x

= 0

6x + 4x

+ 3x

+ 5x

+ 7 x

x1 + 6x2 + 5x3 − 3x4 + 2x5 = 0

+ 2x2

+ x3 + 4x4 + 8x5 = 0

3x1

26.

+ x

= 1

= 0

x + x

− 2x

− x

x1 + x2 + 4x3 + 3x4 = 2

+ x2 + 7 x3 + 5x4 = 3

28.

+ x

= 4

= −1

2x − 3x

+ x

− x

3x1 + 4x2 − 2x3 + 6x4 = 11

+ 4x3

+ 2x4 = 11

5x1

21.

+ x

− x

= 1

= 2

3x + x

+ 2x

− 2x

2x1 − 4x2 − 3x3 + 6x4 = 7

+ 5x2

+ 6x3 − 6x4 = 6

7x1

23.

x1 + 2x2 − 3x3 + x4 = 0x1 + x2 + x3 − x4 = 0

x1 − x2 − x3 + x4 = 0

2x1 + x2 + 4x3 + 5x4 = 0

25.

2x2 + 4x3 − 3x4 − 6 = 0

2x1 + x2 + 3x3 + x4 = 0

6x1 + 5x2 + 13x3 − x4 − 8 = 0

2x1 + 3x2 + 7x3 − 2x4 + 5 = 0

27.
x		+ x		= 1
	1		3
2x1 + 8x2 + 2x3 = 1

16x2 − 10x4 = 21
x + 10x						+ x		+ 10x			= 2
	1				2		3			5
x − 4x				2	+ 6x		3	+ 4x	4		− 2x	5	= −1
	1			2			3		4			5
29.
x		+ x		= 0
	1		3
x1 + x4				= 3
2x + 3x						+ x		= 0
		1			3		5
2x3 + 3x4 + x6 = 7
x		+ 2x			+ 2x			= 0
	1			3			5
		+ 2x3 + 2x6 = −7
x2		+ 2x3 + 2x6 = −7

31.

3x1 + 2x2 − x3 + 3x4 + 5x5 = 06x1 + 4x2 + 3x3 + 5x4 + 7 x5 = 09x1 + 6x2 + x3 + 7 x4 + 9x5 = 03x1 + 2x2 + x3 + 4x4 + 8x5 = 0

33.

x1 − 2x2 − x3 + 3x4 + x5 = 0

3x1 + x2 + 3x3 + 5x4 + 4x5 = 0

x1 − x2 + x3 − 3x4 + 2x5 = 0x1 − 2x2 + x3 + 4x4 + 6x5 = 0

35.

2x1 + x2 + x3 + 4x4 = 13x1 + 4x2 − x3 − x4 = 0

x1 + 5x2 − x3 + x4 = 2

5x1 − 3x2 + 6x3 + 3x4 = 3

37.

3x1 + 4x2 + 5x3 + 7 x4 = 12x1 + 6x2 − 3x3 + 4x4 = 04x1 + 2x2 + 13x3 + 10x4 = 05x1 + 21x3 + 13x4 = 3

30.

2x1 + x2 + 3x3 + x4 = 0

2x2 + 4x3 − 3x4 − 6 = 0

6x1 + 5x2 + 13x3 − x4 − 8 = 02x1 + 3x2 + 7x3 − 2x4 + 5 = 0

32.

x1 − x2 + 2x3 − x4 = 0x1 + x2 − 3x4 − x5 = 0

4x1 − 2x2 + 6x3 + 3x4 − 4x5 = 02x1 + 4x2 − 2x3 + 4x4 − 7x5 = 0

34.

2x + x				− x		− x		+ x		= 0
		1	2	+ x	3	− x	4	− x	5	= 0
x		− 2x		+ x		− x		− x		= 0
	1		2		3		4		5	5.
x1 + 7 x2				− 5x3 − 5x4 + 5x5 = 0

3x1 − x2 − 2x3 + x4 − x5 = 0

36.

x1 − x2 + x3 + x4 − 2x5 = 02x1 + x2 − x3 − x4 + x5 = 1

3x1 + 3x2 − 3x3 − 3x4 + 4x5 = 24x1 − 5x2 − 5x3 − 5x4 + 7x5 = 3

38.

3x1 + 2x2 + x3 − x4 + x5 = 1x1 + 2x2 + 3x3 − x4 = 1

2x1 + 3x2 + x3 + x4 = 1

2x1 + 2x2 + 2x3 − x4 − 2x5 = 1

39.

3x1 − x2 + 2x3 − 7 x4 = 02x1 + 3x2 − x3 + 5x4 = 0

4x1 + x2 − 3x3 + 6x4 = 0

x1 − 2x2 + 4x3 − 7 x4 = 0

41.

2x − 3x					+ 3x				− 2x					= 0
	1			2	− 5x			3	+ 7 x				4	= 0
3x + 4x					− 5x				+ 7 x					= 0
	1			2				3					4
4x1 + 11x2 − 13x3 + 16x4 = 0
		− 2x2 + x3 + 3x4 = 0
7x1		− 2x2 + x3 + 3x4 = 0
43.
2x + x				− x			+ 2x					= 0
	1		2			3					4
x1	− x2 + 2x3 + 3x4 + 4x5 = 0
		+ 2x2 + x3 + x4 + 3x5 = 0
− x1		+ 2x2 + x3 + x4 + 3x5 = 0
x + 5x				− 8x				− 5x					− 12x						= 0
1			2				3					4						5
3x − 7 x				2	+ 8x			3	+ 8x				4	+ 13x					5	= 0
	1			2				3					4						5
45.
2x + x				− x			+ 2x					− 3x					= 0
	1		2	+ x		3	− x				4					5
x	− 2x			+ x			− x				+ x				= 0
1			2			3				4				5
3x1 − 2x2 − x3 + x4 − 2x5 = 0
		− 5x2 + x3 − 2x4 + 2x5 = 0
2x1		− 5x2 + x3 − 2x4 + 2x5 = 0
47.
4x		+ x		+ 3x				= 15
	1		2				3
x1	+ x2 + x3 = 6
		+ 2x2 − x3 = 4
3x1		+ 2x2 − x3 = 4
2x		− x		+ x			= 3
	1		2			3
7x		+ 5x		2	− x		3	= 14
	1			2			3

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