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Гродненский государственный университет им. Я. Купалы

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[НЕСОРТИРОВАННОЕ]

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Контрольная по ВМатем

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<<< < Предыдущая 1 2 3 45 / 185 6 7 8 9 10 11 12 13 14 15 16 17 18 > Следующая >>>

	1		0		2				2		4	3
51.	A = 0		1		1 , B = 4						5	1 ;
	2 1 −1								3 1 2
	−1 0					2			1				5 −2
52.	A = 3		−1			2 ,		B = −2					0	4 ;
	4 −1 −2								−1 6 −2
	2		1	3				2		5		7
53.	A = 4		3	2 ,		B = 6				3		4 ;
	3 2 3							5 −2 −3
54. A = −1				2		−3		0	, BT =			1		1	0	1	;
	3 −1 0 1											2 −2 1 −3
										6			1
	1 2 −2 1									0 1
55.	A = 0		3	−1			5	, B =			0		1	;
											−3		2
											−3		2
	2 −3 −1								−3 2 −1
56.	A = 1		4		0 , B = 0							1		0 ;
	−1 0 3								−1 0 2
	0 −1				0				3 1 0
57.	A = 1			2	0 , B = −3							0		1 ;
	−1 0 3								0 −2 1
	1 −2 0 4									3 −1
58.	A = 0		−1		2	0		,	B =	−1			−2 ;
	1 2 −1									1 −2
59.								B =			4	5
59.	A =	1		3		0	,	B =			4	5	;
		−2		−1 0							7 3
		−2		−1 0							7 3
60.	AT = (1		−2		2		0		2), B = (3					−3	0	2	−1) ;

61.	A =	3 2 1 0						B =	1 0 1 0					;
61.	A =	2		1	0 3 ,			B =	2		1	1	0	;
		3 0				−1		0 1 2
62.	A =		2	−3		−1 , B = 0					−1	1 ;
		1 0 1						1 0 2
		1		0	1			0		1	0
63.	A = 0			1	0 , B = 1					0	1 ;
		1 0 1						0 1 0
		0 1 0 3									0 3 0 2
64.			1	−1		3	1		T				2		;
64.	A =		1	−1		3	1	, B		= 3			2	0 −2	;
		−1 0 1 0									−2 −1 0 0
		1 0 −1						4 0 −2
65.	A = 1			−2		0 , B = 0					1	5 ;
		3 −1 0						4 −1 2
		−2 −1 0						0			1 0
66.	A = 0			1		2 , B = −1					1	−1 ;
		1 0 1						2 0 −1
		0 −3 6						3 1 0
67.	A = 1			−1		0 , B = −3					0	3 ;
		−1 0 3						0 3 1
										7		−1
		1 2 −2 1								0 1
68.	A =	0		1	−1		5	, B =			9	1	;

										−3		1


69.		−1			2			1		−1			;
69.	A = −3				−2	, B =		3		−2			;
		1		0	1			0		1			0
70.	A = 0			1	0 , B = 1					0			1 ;
		1 0 1						0 1 0
		2 4 −1								5 2 1
71.	A = 1			−4		0 , B = 0							1	2 ;
		−1 −2 3								−1 0 2
		3 2 1 0								1 0 1 0
72.	A = 2			1	0	3	,	B =		2			1	1 0 ;
		1		0		2			2				0	1
73.	A = −1			1		1 ,	B = 0						1	0 ;
		2 −1 0							−1 2 2
		−1 4 0 −2									−2 −1 −3 1
74.	A =		1 0 1 0						, B =			−2 1 0 2			;
74.	A =		−2 1 3 3						, B =			1 −2 2 −3			;
			−2 1 3 3									1 −2 2 −3
			−1 2 0 −2									1 4 2 1
			−1 2 0 −2									1 4 2 1
		1 0 0						−2 −2 1
75.	A = 1			1	1 , B = 0						1		0 ;
		2 1 0						3 2 1
		−1			2 0					1			2 3
76.	A = 0				2	−1 ,			B = −2				3 2 ;
		1 −1 1								0 −1 −1

77.	2 −1 4		0	,	T	2	1	−1 −2	;
77.	A =			,	B	=			;
		−1 3 0	−2			5	0	3 3

		0 1 2 −1										T			−12 0 1 2
78.	A =	−2			3	−10			3	,	B			=			0	1		−3 −3 .
		4			1	4		0					1				−5	4
		4			1	4		0					−1					1
79.	A =				−2	0							−1				0	1		;
79.	A =	−1			−2	0	−2 , B =						0				3 0			;
		1 −2 4 9											0				3 0
													−2				3	1
			−4		1	0		0						0			−5		4
			−4		1	0		0							−1 0 −2
80.	A =			1	−2	0				,	B =				−1 0 −2							;
80.	A =			1	−2	0		−2		,	B =			2 3 0								;
			1 −1 4 7											2 3 0
														0			3		1
			0 2 −1 3												2 −1 0 2
81.	A =			1 4 −2 6							,	B =			0 1 −3 1								;
81.	A =			−1 0 0 2							,	B =				−2 0 0 1							;
				−1 0 0 2												−2 0 0 1
				1	−2 0 −2											2 1 0 0
				1	−2 0 −2											2 1 0 0
			0 1 0 1								−1 −1 0 1
82.	A =			1 0 1 0				,	B =		0 1 0 1										;
82.	A =			0 1 0 1				,	B =			−1 0 −1 1									;
				0 1 0 1								−1 0 −1 1
				1 0 1 0								1 1 0 0
				1 0 1 0								1 1 0 0
			1		2 3						−2 3 0
83.	A = −2				3	2 ,			B = −1							0	2
			0 −1 −1								2 −1 0
			4 −2 1								−4 2 1
84.	A = 1				−2	0 ,			B = 1						−2		3 ;
			−1 5 2								0 −1 2

85. A = 1

86. A = 0

87. A = 0

2−1

88. A = 3

89. A = 4

−1

90. A =

91. A =

92. A = 1

−1

−8 2		2	5		7
4	0 , B = 6		3 4 ;
−4 2		5	−2 −3
0 2 1			1 −4 −1 −2
−1 0 1		, B =		0	−1 2 −1	;
1 0 2		, B =		3	−1 −2 2	;
1 0 2				3	−1 −2 2
1 −2 2				1	0 −2 1
1 −2 2				1	0 −2 1
0	2	2	4		3
1	1 , B = 4		5	1 ;
1	−1	3	1	2

0	2			1		5	−2
−1 2 , B = −2 0 4 ;
−1 −2				−1 6 −2
1 3		2		5		7
3 2 , B = 6 3 4 ;
2 3		5 −2 −3
2 −3 0			, BT =			1 1 0 1		;
−1 0 1						2 −2 1 −3
				6		1
2 −2 1				0 1
3 −1 5		,	B =		0 1		;
					−3 2

−3 −1			−3 2 −1
4	0 , B = 0 1 0 ;
0 3			−1 0 2

	0 −1 0							3 1 0
93.	A = 1		2		0 , B = −3							0		1 ;
	−1 0 3							0 −2 1
	1 −2 0 4									3 −1
94.	A = 0		−1	2	0		,	B =		−1			−2 ;
	1 2 −1										1 −2
95.								B =			4	5		;
95.	A =	1	3		0	,		B =			4	5		;
		−2	−1 0								7 3
		−2	−1 0								7 3
96.	AT = (1		−2	2		0		2), B = (3						−3	0	2 −1) ;
97.	3 2 1 0								1 0 1 0						;
97.	A = 2		1	0 3 ,			B =		2			1	1	0	;
	3 0			−1				0 1 2
98.	A =	2	−3	−1 , B = 0							−1		1 ;
	1 0 1							1 0 2
	1		0	1			0			1	0
99.	A = 0		1	0 , B = 1						0	1 ;
	1 0 1						0 1 0
		0 1 0 3											0 3 0 2
100. A =					3					T	=		3	2	0
100. A =		1 −1			3		1 ,		B		=		3	2	0	−2 .
		−1 0 1 0										−2 −1 0 0

Задача 3. Даны векторы a, b, c . Проверить, что векторы a, b, c об-

разуют базис и найти координаты вектора d в этом базисе. Вычислить скалярное и векторное произведение векторов a , b .

Вариант
	a	b	c	d

1	(1,0,1)	(3,4,5)	(3,8,1)	(4,0,2)
2	(-1,2,0)	(-3,2,4)	(0,0,1)	(6,5,-4)
3	(6,0,-1)	(2,4,1)	(3,3,1)	(-2,5,7)
4	(1,-3,2)	(5,0,2)	(-2,4,1)	(8,1,3)
5	(2,1,1)	(-3,-1,5)	(2,4,3)	(6,1,2)
6	(6,3,2)	(7,4,-5)	(4,2,2)	(4,1,2)
7	(1,-1,1)	(2,1,3)	(1,-2,2)	(6,8,1)
8	(3,0,4)	(6,3,4)	(1,2,3)	(-3,4,-2)
9	(7,2,1)	(-1,2,1)	(4,3,0)	(5,-3,7)
10	(2,5,6)	(1,2,2)	(1,0,1)	(3,2,2)
11	(1,0,1)	(3,4,5)	(3,8,1)	(5,2,7)
12	(-1,2,0)	(-3,2,4)	(0,0,1)	(4,3,-1)
13	(6,0,-1)	(2,4,1)	(3,3,1)	(3,9,2)
14	(1,-3,2)	(5,0,2)	(-2,4,1)	(2,-1,-3)
15	(2,1,1)	(-3,-1,5)	(2,4,3)	(3,-1,4)
16	(6,3,2)	(7,4,-5)	(4,2,2)	(5,1,7)
17	(1,-1,1)	(2,1,3)	(1,-2,2)	(2,-8,1)
18	(3,0,4)	(6,3,4)	(1,2,3)	(-1,5,-3)
19	(7,2,1)	(-1,2,1)	(4,3,0)	(2,-2,2)
20	(2,5,6)	(1,2,2)	(1,0,1)	(4,3,2)
21	(1,0,1)	(3,4,5)	(3,8,1)	(-2,4,1)
22	(-1,2,0)	(-3,2,4)	(0,0,1)	(6,3,-1)
23	(6,0,1)	(2,4,1)	(3,3,1)	(8,-5,1)
24	(1,-3,2)	(5,0,2)	(-2,4,1)	(6,-1,2)
25	(2,1,1)	(-3,-1,5)	(2,4,3)	(7,8,-4)
26	(6,3,2)	(7,4,-5)	(4,2,2)	(5,4,3)
27	(1,-1,1)	(2,1,3)	(1,-2,2)	(-1,5,1)
28	(3,0,4)	(6,3,4)	(1,2,3)	(3,-2,-2)
29	(7,2,1)	(-1,2,1)	(4,3,0)	(9,-1,1)
30	(2,5,6)	(1,2,2)	(1,0,1)	(4,2,0)
31	(3,4,5)	(1,0,1)	(3,8,1)	(4,0,2)
32	(-3,2,4)	(-1,2,0)	(0,0,1)	(6,5,-4)
33	(2,4,1)	(6,0,-1)	(3,3,1)	(-2,5,7)

34	(5,0,2)	(1,-3,2)	(-2,4,1)	(8,1,3)
35	(-3,-1,5)	(2,2,1)	(2,4,3)	(6,1,2)
36	(7,4,-5)	(6,3,2)	(4,2,2)	(4,1,2)
37	(2,1,3)	(1,-1,1)	(1,-2,2)	(6,8,1)
38	(6,3,4)	(3,0,4)	(1,2,3)	(-3,4,-2)
39	(-1,2,1)	(7,2,1)	(4,3,0)	(5,-3,7)
40	(1,2,2)	(2,5,6)	(1,0,1)	(3,3,2)
41	(3,4,5)	(1,0,1)	(3,8,1)	(5,2,7)
42	(-3,2,4)	(-1,2,0)	(0,0,1)	(4,3,-1)
43	(2,4,1)	(6,0,-1)	(3,3,1)	(3,9,2)
44	(5,0,2)	(1,-3,2)	(-2,4,1)	(2,-1,-3)
45	(-3,-1,5)	(2,1,1)	(2,4,3)	(3,-1,4)
46	(7,4,-5)	(6,3,2)	(4,2,2)	(5,1,7)
47	(2,1,3)	(1,-1,1)	(1,-2,2)	(2,-8,1)
48	(6,3,4)	(3,0,4)	(1,2,3)	(-1,5,-3)
49	(-1,2,1)	(7,2,1)	(4,3,0)	(2,-2,2)
50	(1,2,2)	(2,5,6)	(1,0,1)	(4,3,2)
51	(3,4,5)	(1,0,1)	(3,8,1)	(-2,4,1)
52	(-3,2,4)	(-1,2,0)	(0,0,1)	(6,3,-1)
53	(2,4,1)	(6,0,1)	(3,3,1)	(8,-5,1)
54	(5,0,2)	(1,-3,2)	(-2,4,1)	(6,-1,2)
55	(-3,-1,5)	(2,1,1)	(2,4,3)	(7,8,-4)
56	(7,4,-5)	(6,3,2)	(4,2,2)	(5,4,3)
57	(2,1,3)	(1,-1,1)	(1,-2,2)	(-1,5,1)
58	(6,3,4)	(3,0,4)	(1,2,3)	(3,-2,-2)
59	(-1,2,1)	(7,2,1)	(4,3,0)	(9,-1,1)
60	(1,2,2)	(2,5,6)	(1,0,1)	(4,2,0)
61	(3,8,1)	(4,0,2)	(3,4,5)	(1,0,1)
62	(0,0,1)	(6,5,-4)	(-3,2,4)	(-1,2,0)
63	(3,3,1)	(-2,5,7)	(2,4,1)	(6,0,-1)
64	(-2,4,1)	(8,1,3)	(5,0,2)	(1,-3,2)
65	(2,4,3)	(6,1,2)	(-3,-1,5)	(2,2,1)
66	(4,2,2)	(4,1,2)	(7,4,-5)	(6,3,2)
67	(1,-2,2)	(6,8,1)	(2,1,3)	(1,-1,1)
68	(1,2,3)	(-3,4,-2)	(6,3,4)	(3,0,4)

69	(4,3,0)	(5,-3,7)	(-1,2,1)	(7,2,1)
70	(1,0,1)	(3,3,2)	(1,2,2)	(2,5,6)
71	(3,8,1)	(5,2,7)	(3,4,5)	(1,0,1)
72	(0,0,1)	(4,3,-1)	(-3,2,4)	(-1,2,0)
73	(3,3,1)	(3,9,2)	(2,4,1)	(6,0,-1)
74	(-2,4,1)	(2,-1,-3)	(5,0,2)	(1,-3,2)
75	(2,4,3)	(3,-1,4)	(-3,-1,5)	(2,1,1)
76	(4,2,2)	(5,1,7)	(7,4,-5)	(6,3,2)
78	(1,-2,2)	(2,-8,1)	(2,1,3)	(1,-1,1)
79	(1,2,3)	(-1,5,-3)	(6,3,4)	(3,0,4)
80	(4,3,0)	(2,-2,2)	(-1,2,1)	(7,2,1)
81	(1,0,1)	(4,3,2)	(1,2,2)	(2,5,6)
82	(3,8,1)	(-2,4,1)	(3,4,5)	(1,0,1)
83	(0,0,1)	(6,3,-1)	(-3,2,4)	(-1,2,0)
84	(3,3,1)	(8,-5,1)	(2,4,1)	(6,0,1)
85	(-2,4,1)	(6,-1,2)	(5,0,2)	(1,-3,2)
86	(2,4,3)	(7,8,-4)	(-3,-1,5)	(2,1,1)
87	(4,2,2)	(5,4,3)	(7,4,-5)	(6,3,2)
88	(1,-2,2)	(-1,5,1)	(2,1,3)	(1,-1,1)
89	(1,2,3)	(3,-2,-2)	(6,3,4)	(3,0,4)
90	(4,3,0)	(9,-1,1)	(-1,2,1)	(7,2,1)
91	(3,8,1)	(5,2,7)	(1,0,1)	(3,4,5)
92	(0,0,1)	(4,3,-1)	(-1,2,0)	(-3,2,4)
93	(3,3,1)	(3,9,2)	(6,0,-1)	(2,4,1)
94	(-2,4,1)	(2,-1,-3)	(1,-3,2)	(5,0,2)
95	(2,4,3)	(3,-1,4)	(2,2,1)	(-3,-1,5)
96	(4,2,2)	(5,1,7)	(6,3,2)	(7,4,-5)
97	(1,-2,2)	(2,-8,1)	(1,-1,1)	(2,1,3)
98	(1,2,3)	(-1,5,-3)	(3,0,4)	(6,3,4)
99	(4,3,0)	(2,-2,2)	(7,2,1)	(-1,2,1)
100	(3,8,1)	(5,2,7)	(2,5,6)	(3,4,5)

Задача 4. Решить систему методом Крамера и матричным методом.

x + x + x = −2

1 2 3

1.2x1 − 3x2 − x3 = −6

3x1 + 4x2 + 3x3 = −5

3x + x + x = 8

1 2 3

3.2x1 − 3x2 + 2x3 = 2

x1 + 2x2 − x3 = 2

x + 2x − 4x = −7

1 2 3

2.2x1 − 3x2 + 5x3 = 113x1 − x2 + 5x3 = 16

2x + 3x − x = 4

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

2x1 + 3x2 + 4x3 = 3

2x − x + 5x = 4

1 2 3

9.5x1 + 2x2 + 13x3 = 23x1 − x2 + 5x3 = 0

x + 3x = −6

2 3

11.x1 − 2x2 − x3 = 5

3x1 + 4x2 − 2x3 = 13

x + 2x − x = 2

1 2 3

13.2x1 − 3x2 + 2x3 = 2

3x1 + x2 + x3 = 8

x + 2x + 3x = 6

1 2 3

15.2x1 + 3x2 − x3 = 43x1 + x2 − 4x3 = 0

2x + 4x + x = 4

1 2 3

17.3x1 + 6x2 + 2x3 = 44x1 − x2 − 3x3 = 1

	x − x		− 3x	= 13
	1	2	3
19.	2x1 + x2 − x3			= 0
		− 2x2 + 4x3 = −15
	3x1	− 2x2 + 4x3 = −15
	x + 2x		+ x = 1
	1	2	3
6.	x2 − x3 = −3

	4x1 + 2x2 − x3 = 0

x − x − x = 0

1 2 3

8.x1 + 2x2 + x3 = 1

x2 − x3 = −3

x + 5x + x = 0

1 2 3

10.2x1 − 4x2 − 3x3 = −13x1 + 4x2 + 2x3 = 8

4x1 + 2x2 − x3 = 0

12. x1 + 2x2 + x3 = 8

x2 − x3 = −3

<<< < Предыдущая 1 2 3 45 / 185 6 7 8 9 10 11 12 13 14 15 16 17 18 > Следующая >>>

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