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Рязанский государственный радиотехнический университет

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Тр номер 1(математика)

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	1	3	0		7 0		−5
	−2	1			−4	2	1
8.29. A =			−3 ,	B =				.
	6	2	0		−1	3	6

	−3		1
8.30. A =		2	−2			0			−5 3 1
8.30. A =				,	B =							.
		4	0						2
		4	0			7			2		0 3
		−1	5
		−1	5
							3			−4
8.31. A =	−1		−2 7 0		,	B =		2		−	1
8.31. A =					,	B =						.
		4						−5 1
		4	−3 1 −1					−5 1
								0		−	3
б)								0		−	3
б)							1		−5
8.1. f (x)= 2x2			−5x + 2 , если A =				1		−5
8.1. f (x)= 2x2			−5x + 2 , если A =							.

							2			3
8.2. f (x)= 3x2			+ x −4 , если A			5		−3
8.2. f (x)= 3x2			+ x −4 , если A			=				.
							0		1
							0		1
8.3. f (x)= x3 + 2x						1		2
8.3. f (x)= x3 + 2x				, если A =				.
						−2
						−2		0
8.4. f (x)= 2x2								0		2
8.4. f (x)= 2x2			−3x −1 , если A =							.

						−3				1
8.5. f (x)= x2 −3x +1 , если A						1		−4
8.5. f (x)= x2 −3x +1 , если A						=				.
									3
						0			3
8.6. f (x)= −2x			2 −3x −9 , если A =					3		−2
8.6. f (x)= −2x			2 −3x −9 , если A =								.
										0
								1		0
8.7. f (x)= 4x2			+5x −3 , если A =				3			0
8.7. f (x)= 4x2			+5x −3 , если A =							.
								−1
								−1		2

21							22
8.8. f (x)= −x2		+ 4x −3 , если A =			1	2
8.8. f (x)= −x2		+ 4x −3 , если A =				.

			−2			0
8.9. f (x)= 5x2		3			−	2
8.9. f (x)= 5x2		− x +7 , если A =				.
			0
			0		1
8.10.		3			−1
8.10.	f (x)= −x2 +8x , если A =					.

		2			−4
8.11.	f (x)= x2	−3x +5 , если A =	−		1	1
8.11.	f (x)= x2	−3x +5 , если A =					.
				3
				3		−4
8.12.	f (x)= −2x2 +3x + 2 , если A =				−	4	2
8.12.	f (x)= −2x2 +3x + 2 , если A =						.

					0		5
8.13.	f (x)= 3x	2 + 4x −3, если A =		−1		2
8.13.	f (x)= 3x	2 + 4x −3, если A =					.
					3	−
					3	−	4
8.14.	f (x)= −x2 +5x +1, если A =			2		−3
8.14.	f (x)= −x2 +5x +1, если A =						.
						1
				3		1
8.15.	f (x)= −4x2 + 2x −5 , если A =				−	2	1
8.15.	f (x)= −4x2 + 2x −5 , если A =						.

					5		0
8.16.	f (x)= x2	−2x +3 , если A =	1		−2
8.16.	f (x)= x2	−2x +3 , если A =				.
				2
				2		0
8.17.	f (x)= −2x2 + 4x −3 , если A =				5	−3
8.17.	f (x)= −2x2 + 4x −3 , если A =						.

					1	2
8.18.	f (x)= 2x	2 − x +1 , если A =	1			−1
8.18.	f (x)= 2x	2 − x +1 , если A =					.
				−3		2
				−3		2
8.19.	f (x)= 5x	2 −3x +3 , если A =		3		−4
8.19.	f (x)= 5x	2 −3x +3 , если A =					.
						2
				1		2
8.20.	f (x)= −x2 + 2x −1, если A =			−1		3
8.20.	f (x)= −x2 + 2x −1, если A =						.
						0
				−2		0

8.21.	f (x)= 4x2		−3x + 2 , если A =			4		−1
8.21.	f (x)= 4x2		−3x + 2 , если A =					.
							2
							2	3
8.22.	f (x)= −3x		2 − x + 2 , если A =			3		−1
8.22.	f (x)= −3x		2 − x + 2 , если A =					.
							2
							2	0
8.23.				−1				4
8.23.	f (x)= x2 − x + 2 , если A =							.
					5
					5		−2
8.24.	f (x)= −2x		2 + 2x −3 , если A =				2	1
8.24.	f (x)= −2x		2 + 2x −3 , если A =					.

							1	−3
8.25.	f (x)= 3x2		− x + 2 , если A =			1		2
8.25.	f (x)= 3x2		− x + 2 , если A =					.
						−2
						−2		3
8.26.	f (x)= −x2		+3x −4 , если A =			0		3
8.26.	f (x)= −x2		+3x −4 , если A =					.
							1
							1	−2
8.27.	f (x)= x2 −4x +3 , если A =				4			−1
8.27.	f (x)= x2 −4x +3 , если A =							.
						−5
						−5		2
8.28.	f (x)= −3x		2 + x −1 , если A =			2		−1
8.28.	f (x)= −3x		2 + x −1 , если A =					.

						3		5
8.29.				−1				1
8.29.	f (x)= x2 − x +6 , если A =							.
					3
					3		−1
8.30.	f (x)= −x2		+5x −1, если A =			3		1
8.30.	f (x)= −x2		+5x −1, если A =					.

						0		2
8.31.	f (x)= 3x2		−3x + 4 , если A =			−2		0
8.31.	f (x)= 3x2		−3x + 4 , если A =					.
							1
в)							1	−1
в)
	2 −1 5							−2 5 1
		0	3 1						0	−3 4
8.1. A =		0	3 1			8.2. A =			0	−3 4	.
		−4 6 2							0	1 2
		−4 6 2							0	1 2

−3			1	5
		0	4	0
8.3. A =
	−5		2	2

1			2	−3
	3		2	−	4
8.5. A =
	2		−1	0

5			6	3
	0		2	0
8.7. A =
	7		−4	5

1			2	−1
	3		0	2
8.9. A =
	4		−2	5

	2		−1		−1
8.11. A =		3	4	−			2

		3	−2			4

	1		2	4
8.13. A =		5	1	2

		3	−1	1

	4		−1		2
8.15. A =		0	2
				−3
		0	−1		4

	2		3				1
8.17. A =		−1 −5				−		2

		4	1				2

1			−2	3
	2		0	5
8.4. A =						.
	1		−1	2

	2		−3	1
	4		−5	2
8.6. A =						.
	5		−7	3

		3	0		2
	−5		3	−
8.8. A =						1 .
		6	0
					3
	1		1	2
8.10. A =		0	3	1
					.
		4	1	4

	3		2	1
8.12. A =		2	3	1
					.
		2	1
				3
	1		2	3
8.14. A =		0	2	4
					.
		0	0	2

1		−2		−6
		5		1
8.16. A = −4		5		1	.
	2	0		−2
	2	0		−2
	3	2	0
	−3	1	5
8.18. A =	−3	1	5	.
	−2	0	1
	−2	0	1

4			−5		2
	−1		1
8.19. A =					−1
	3		2		0

2			2	3
	1		−1	0
8.21. A =
	−1		2	1

	4		1	1
	−4		2	0
8.23. A =
	1		2	1

1		2	1
	2	1	2
8.25. A =
	1	2	3

−6			2	0
	0		4	2
8.27. A =
	0		2	6

	2	3	1
	0	1	2
8.29. A =
	3	1	1

−3			−2			1
	2		−1			0
8.31. A =							.
	3		4
					−1

	2	4 −6
	0	2	4
8.20. A =				.
	0	0	2

1		1	−1
	2	1	0
8.22. A =					.
	1	−1	1

−3		1	0
	0	2	1
8.24. A =				.
	0	1	3

3		1	−2
	3	−2	4
8.26. A =					.
	3	5
			−1
	4	0			2
	−4	6			2
8.28. A =						.
	8	−2		10

−2		3	5
	0	3	0
8.30. A =				.
	−4	5	2

Задача 9. Используя формулы Крамера, решить системы линейных алгебраических уравнений.

x1 + x2 + 2x3 = −4,		2x1 + x2 + x3 = 2,
	+ x3 = 3,		+ 2x2	+5x3	= 7,
9.1. 2x1 + x2		9.2. 4x1
	+3x3 = −1.		+5x2	+3x3	=8.
x1 +3x2		7x1

x + x +3x = 7,

9.3.2x1 +3x2 + x3 =10,x1 + 4x2 − x3 = 6.1 2 3

=12,

9.5.2x1 + x2 − x3 = 5,x1 −2x2 −3x3 = −20.x1 + x2 + x3

=0,

9.7.x1 + 2x2 −5x3 = −3,x1 −2x2 + 4x3 = 2.5x1 + x2 − x3

=−2,

9.9.3x1 +6x2 + x3 = −10,x1 + x2 −4x3 = −8.2x1 + 2x2 − x3

=4,

9.11.2x1 −5x2 + 2x3 =1,

x1 − x2 − x3 = −2.x1 +5x2 − x3

=−11,

9.13.2x1 − x2 − x3 = 3,x1 −2x2 + 4x3 =18.x1 + 2x2 −3x3

x + 2x +3x = 4,

9.15.2x1 −3x2 −4x3 =1,x1 +5x2 −5x3 = 7.1 2 3

=10,

9.17.x1 − x2 −3x3 = −4,

2x1 −5x2 + 2x3 =8.2x1 +5x2 +3x3

=1,

9.4.x1 +3x2 −4x3 = −16,2x1 + x2 +3x3 =11.x1 + 2x2 + x3

=6,

9.6.3x1 − x2 + x3 = 4,x1 +3x2 + 4x3 =12.2x1 + 2x2 + x3

=−2,

9.8.x1 −2x2 +5x3 = 6,2x1 − x2 − x3 = 4.x1 −2x2 −3x3

x1 + 2x2 −3x3 = −4,

9.10. x1 + x2 + x3 =12,2x1 − x2 + x3 = 7.

=−9,

9.12.x1 + x2 −7x3 = −6,

5x1 − x2 −2x3 = −3.3x1 −3x2 −6x3

x + 2x + x = 4,

9.14.− x1 −2x2 −2x3 = −5,

2x1 +7x2 −9x3 = 0.1 2 3

=−3,

9.16.2x1 + 2x2 +3x3 = 3,x1 +3x2 −3x3 = −1.x1 + x2 + x3 =1,

9.18.x1 −2x2 +3x3 = 6,x1 + x2 +5x3 = 5.x1 − x2 − x3

=9,

9.19.2x1 −5x2 − x3 = −4,x1 + 4x2 −5x3 = 0.x1 +5x2 +3x3

=−4,

9.21.2x1 + x2 + 2x3 =1,x1 + 4x2 −5x3 = −2.x1 − x2 −2x3

x − x +5x = 7,

9.23.2x1 + x2 − x3 = 0,x1 +3x2 + 4x3 = 2.1 2 3

2x1 + x2 +5x3 = 5, 9.25. x1 + 2x2 −5x3 = 4,

3x1 −2x2 −7x3 = 4.

=−1,

9.27.2x1 −2x2 + 2x3 = 2,x1 − x2 −5x3 = 7.x1 + x2 + x3

=−2,

9.29.x1 + 2x2 −5x3 = −3,2x1 + 2x2 + 2x3 = −4.x1 + x2 +5x3

x + x + x = 4,

9.31.2x1 −3x2 + x3 = −3,

x1 + x2 − x3 =1.1 2 3

2x + x + x = 5,

9.20.x1 − x2 +5x3 =1,3x1 + 2x2 +7x3 =8.2x1 + 2x2 +3x3 =10,

9.22.x1 −3x2 + 4x3 =10,3x1 +5x2 + 2x3 =10.1 2 3

=1,

9.24.3x1 −3x2 + 4x3 = 4,x1 −3x2 −3x3 = −5.x1 +3x2 −3x3

=18,

9.26.−2x1 −3x2 + x3 = −2,

x1 +3x2 +3x3 =8.7x1 − x2 − x3 = 4,

9.28.5x1 + x2 + x3 =8,

x1 −7x2 − x3 = −8.

− x1 +7x2 − x3 = 2,

9.30.−2x1 + x2 −3x3 = 5,x1 −5x2 +3x3 = −4.2x1 + x2 +7x3

Задача 10. Исследовать СЛАУ. Определить совместность систем и найти решение, если система совместна.

x1 + 2x2 −3x3 + 4x4 = −9,

10.1. а) − x1 − x2 +3x3 −6x4 =14,2x1 + 4x2 −5x3 +9x4 = −17,

2x1 +5x2 −6x3 +9x4 = −16,x1 −2x2 + 4x3 −16x4 = 21,

2x1 + x2 + 4x3 +6x4 = 45, б) 2x1 + 2x2 +3x3 +14x4 = 44,

x1 + x2 + 2x3 +6x4 = 26,2x1 − x2 +3x3 + 4x4 = −3,

в) −2x1 +5x3 +5x4 =1,6x1 −2x2 + x3 +3x4 = 5,4x1 + x2 + 2x3 + x4 = −4.x1 +3x2 + 2x3 −3x4 = 0,

10.2. а) 2x1 + 2x2 −3x3 + 4x4 = −16,3x1 +5x2 + 4x3 + 2x4 =15,

− x1 + 2x2 + 2x3 +3x4 = 4,x1 + 2x2 +5x3 −3x4 = 7,

б) 2x1 +5x2 +11x3 −8x4 =16,x1 + x2 + 4x3 − x4 = 5,

3x1 +6x2 +15x3 −9x4 = 21,x1 + 2x2 − x3 +5x4 = −1,

в) 3x1 + x2 + 4x3 +5x4 = 0,

−2x1 +3x2 +6x3 + 4x4 = −2,4x1 +7x2 +5x3 +18x4 =1.

x1 + 4x2 −3x3 + 2x4 = −3,

10.3. а) −2x1 +3x2 + x3 −2x4 = 5,4x1 +5x2 −3x3 + x4 = 21,

2x1 + x2 + x3 +3x4 = 5,2x1 + 2x2 + x3 + x4 = 9,

б) 4x1 + x2 + 2x3 − x4 =12,2x1 +3x2 − x3 −8x4 = 5,

−2x1 + x2 +3x3 + 22x4 = 9,3x1 − x2 +3x3 + x4 =1,

в) x1 + 2x2 +5x4 = 0,

−2x1 +5x2 + x3 +8x4 = 4,4x1 +3x3 + 4x4 =1.

2x1 −5x2 +3x3 − x4 = 0,

10.4. а) − x1 +3x2 + x3 + 4x4 = 6,

4x1 + 2x3 + x4 =1,

2x1 +7x2 −4x3 +3x4 =12,2x1 +3x2 − x3 −7x4 = −4,

б) −2x1 −5x2 +3x3 +5x4 = 4,4x1 +3x2 + x3 −17x4 = −8,−4x1 −7x2 +3x3 +13x4 =8,− x1 + x2 + x3 +3x4 = 2,

в) 6x1 −5x2 + x3 −2x4 = 3,2x1 + x2 +3x3 + 2x4 = 3,

4x1 −2x2 + 2x3 =1.

29		30
x1 + x2 +8x3 −3x4 =8,
	+ x2 −7x3	−5x4 =12,
10.5. а) 3x1
−3x1 +6x2 + x3 −4x4 = 5,
	−2x2 +6x3 +3x4 = −13,
2x1
x1 +3x2 + x3 + 2x4 = −2,
	+ 2x2 + x4	= −9,
2x1
б)	+ 2x3 + x4	= 23,
2x1
		+3x4 = 21,
x1 +3x2 +3x3

x1 −3x2 + x3 + 2x4 = 4,

в) −5x1 +3x2 + 2x3 +3x4 = 7,x1 + x2 −2x3 + x4 = 4,

−2x1 + 2x2 + 2x4 = 3.x1 +6x2 + 2x3 − x4 =13,

10.6. а) 8x2 +5x3 + 2x4 =15,− x1 + 4x3 +3x4 = −5,

2x1 + 2x2 −3x3 +3x4 = −7,3x1 +8x2 + x3 +5x4 =19,

б) 4x1 +17x2 −2x3 +3x4 = 25,x1 −3x2 + 2x3 + x4 = 4,

−2x1 −6x2 +3x3 +7x4 = −6,x1 + x2 +3x3 + 2x4 = 3,

−3x1 + x2 + x3 +3x4 = 2, в) 5x1 −7x2 +3x3 −2x4 = 5,

2x1 −2x2 + 2x3 =1.

5x1 +6x2 + 4x3 + x4 = 3,

10.7. а) 5x1 +3x2 +5x3 +3x4 = −2,x1 −2x2 +5x3 −3x4 = 5,

3x1 − x2 −2x3 + 4x4 = 5,x1 −2x2 + 2x3 −2x4 = −3,

б) 3x1 −13x2 − x3 + x4 = −2,−4x1 +15x2 − x3 + x4 = 5,

−2x1 +5x2 −4x3 + 2x4 = 6,9x1 −5x2 −7x3 +8x4 = 6,

3x1 + 2x2 + 4x3 −5x4 = 2, в) 2x1 +5x2 +9x3 −11x4 = 2,

x1 −2x2 +3x4 = 5.

x1 + x2 + 4x3 + 2x4 = −1,

10.8. а) 3x1 −2x2 −5x3 −2x4 = 3,−7x1 − x2 −2x3 + x4 =10,

6x1 + x2 +3x3 +5x4 =17,3x1 + x2 −2x3 −7x4 = 9,

− x1 +6x2 +7x3 +15x4 =16, б) x1 +5x2 + 4x3 +7x4 =17,

3x1 +9x2 +6x3 +9x4 = 33,

3x1 −5x2 + 2x3 + 4x4 = 2,− x1 −6x2 +3x3 +5x4 =1, в) 5x1 +7x2 −4x3 −6x4 = 3,

2x1 − x2 + x3 = 4.

31 32

x1 +10x2 +3x3 +6x4 =10,

10.9. а) −2x1 + 2x2 + x3 + 4x4 = 5,2x1 + 2x2 + 2x3 +5x4 = 9,

5x1 −6x2 −2x3 −7x4 = −10,

x1 + 4x2 +6x3 +6x4 = 0,− x1 +6x2 + 4x3 +9x4 = −2,

б) 2x1 −2x2 + 2x3 −3x4 = 2,5x1 +10x3 = 4,

x1 + x2 +3x3 + x4 = 7,

3x + 4x − x + 2x = −5, в) 3x1 + 4x2 + x3 +7x4 = 5,

1 2 3 4

5x1 +6x2 + x3 −6x4 = −10.x1 +3x2 + 4x3 −4x4 = −4,

10.10. а) 3x1 + 4x2 + 2x3 −5x4 = 0,2x1 +3x2 + 4x3 + 4x4 =1,

4x1 + 2x2 −4x3 −7x4 = 3,x1 + 2x2 + 2x3 +11x4 = 5,

б) 3x1 −4x2 − x3 +8x4 = −9,5x1 + 2x2 + x3 +18x4 = −1,

2x1 − x2 −3x3 −8x4 = −9,x1 −3x2 −2x3 = −1,

3x1 + x2 + 4x3 −3x4 = −3, в) 2x1 −6x2 −4x3 +5x4 = 6,

2x1 − x2 + x3 + 2x4 = 2.

x1 + 2x2 +5x3 −3x4 =1,

10.11. а) 2x1 −2x2 +7x3 +3x4 = 2,−3x1 − x2 +3x3 −2x4 = 4,

4x1 + x2 +3x3 + 2x4 = −3,

x1 −2x2 + x3 −7x4 = 6,3x1 + x2 + x3 −5x4 = −4,

б) 2x1 + 2x2 +3x3 −3x4 = −15,x1 −2x2 + x3 −7x4 = 6,

x1 +5x2 + x3 =1,

в) 3x1 + 4x2 + 2x3 +5x4 =1,2x1 − x2 + x3 +5x4 = 5,

3x1 −2x2 + 4x3 +3x4 = 2.x1 +5x2 + 4x3 + 4x4 = −2,

10.12. а) −2x1 +3x2 + x4 =1,

4x1 +7x2 + 2x3 −2x4 = 4,x1 +5x2 −4x3 −3x4 = −5,x1 − x2 + x3 +6x4 = 3,

б) 5x1 +3x2 + x3 + 2x4 = 3,7x1 +3x2 −3x3 =1,

x1 + 2x2 + 2x3 − x4 =1,x1 +6x2 −3x3 −5x4 = 0,

в) 2x1 −11x2 +5x3 +9x4 = 2,7x1 + x3 +3x4 = 4,

4x1 + x2 − x3 − x4 = 3.

x1 + 2x2 − x3 +6x4 =1,

+ 4x2 −5x3 + 2x4 = −2,

10.13. а) 6x1

2x1 +3x2 + 4x3 −6x4 = −3,

+ 2x

+3x

−10x

= −1,

x1 + 2x2 +8x3 −4x4 = 7,

+ x2 +7x3 + 4x4 =11,

2x1

б)

−3x2 −10x3 +3x4 = 5,

3x1

−3x2 −11x3 + 2x4 =1,

2x1

x1 + x2 −3x3 −6x4 = 5,

+7x2 +3x3 + 2x4 =1,

в) 3x1

2x1 + 4x2 + x3 +7x4 = 2,

+5x

−2x

+ x

x1 + x2 + x3 + 2x4 =17,

+3x2 −2x3 + x4 = −4,

2x1

10.14. а)

+ x2 −5x3 + 2x4 = 21,

3x1

− x

−3x

= 5,

x1 −2x2 −2x3 + x4 =1,

+5x2 +12x3 − x4 =14,

б) 3x1

2x1 +3x2 +7x3 − x4 = 9,

−2x1 +5x2 +17x3 +9x4 = −1,

x1 +6x2 −3x3 −5x4 =1,

− x2 +5x3 +9x4 = 2,

2x1

в)

11x1 −3x2 + 2x4 = 7,

+ x2 − x3 − x4 = 3.

4x1

x1 + x2 + x3 = 4,

10.15. а) 5x1 +3x2 +5x3 − x4 = −3,5x1 + 2x2 +3x3 + x4 =14,

x1 + 2x2 + 2x3 − x4 = −2,x1 + 2x2 + x3 +7x4 = 5,

3x1 −2x2 +5x3 +17x4 = −11, б) 4x1 + x2 + 2x3 +17x4 =1,

2x1 −3x2 + 4x3 +11x4 = −13,x1 + 2x2 −2x3 +5x4 = 3,

в) 4x1 +3x2 + x3 +17x4 = 2,2x1 + x2 + x3 +9x4 = −1,

2x1 +5x2 +3x3 −7x4 = 4.x1 −2x2 − x3 −3x4 =15,

10.16. а) 2x1 +3x2 + x3 +3x4 = −2,3x1 +8x2 + x3 +5x4 = −23,

4x1 +7x2 +5x3 +14x4 = −5,

2x1 + x2 + x3 +3x4 = 3,x1 + 2x2 + x3 + x4 = 3,

б) 3x1 + 4x2 + 2x3 + 2x4 = 5,5x1 +5x2 + 2x3 = 2,

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

в) 2x1 −3x2 + 4x3 +5x4 = 7,9x1 −9x2 +6x3 +16x4 = 2.

35								36
x1 + x2 + x3 − x4 =14,
		−2x2 + 21x3 + 4x4 = −55,
10.17. а) 3x1
5x1 +6x2 +5x3 −2x4 = 47,
		+ x2 −2x3 =19,
2x1
2x1 + x2 −5x3 +3x4 = 2,
		+ 2x2 − x3 + 2x4 = 2,
2x1
б)		+ 4x2 −11x3 +9x4 =11,
6x1
		+3x2 +3x3 + 2x4 = 7,
2x1
x1 −3x2 +3x3 −4x4 =1,
		− x2 + x3 −2x4 = 4,
в) 5x1
5x1 + x2 − x3 + 2x4 = −2,
3x		−2x	2	+ 2x	3	−3x	4	=1.
	1
x1 +3x2 + 4x3 +8x4 = 3,
		+ 2x2 + x3 +7x4 =8,
10.18. а) 3x1
4x1 + x2 +3x3 + 2x4 =17,
		−5x2 +7x3 +9x4 = −27,
4x1
2x1 +3x2 +10x4 = 5,
		+ 2x2 − x3 −9x4 = 2,
4x1
б)		+ 4x2 −2x3 +17x4 = 5,
6x1
		+ x2 −2x3 +6x4 =1,
2x1

x1 −2x2 + 2x3 +3x4 = 5,

в) −2x1 + x2 +3x3 + 4x4 = 2,3x1 +3x2 −5x3 − x4 = −3,

3x1 +6x2 −2x3 +9x4 = 5.

x1 − x2 + 2x3 −3x4 = 2,

10.19. а) 3x1 + x2 + 4x3 + 2x4 = −8,2x1 −3x2 +7x3 + x4 = −12,

3x1 −5x2 −3x3 + 2x4 = −20,3x1 −6x2 +7x3 +7x4 = 3,

2x1 −4x2 −2x3 −2x4 = 2, б) 4x1 −8x2 +8x3 +8x4 = 4,

x1 −2x2 +5x3 +5x4 =1,x1 −3x2 +3x3 −7x4 = −2,

2x1 + x2 + 2x3 +5x4 = 7, в) 3x1 + 2x2 +3x3 +8x4 = 6,

4x1 − x2 +6x3 + x4 = 5.2x1 + 2x2 +3x3 + 4x4 = 4,

10.20. а) 5x1 + 4x2 +5x3 +5x4 = −1,x1 + 4x2 + 2x4 = −1,

9x1 +6x2 +8x3 +7x4 = −3,x1 +7x2 +3x3 + x4 = −11,

б) 2x1 + 4x2 +3x3 −2x4 = −10,x1 + x2 + 2x3 −3x4 =1,

x1 + 2x2 +3x3 −4x4 = 4,3x1 + x2 − x3 +3x4 =1,

x1 −3x2 +3x3 + 4x4 =1, в) 3x1 −4x2 + 4x3 −5x4 = 5,

2x1 +3x2 −3x3 +5x4 = −3.

37								38
−2x1 + x2 + 22x3 −7x4 = −40,
	+3x2 +6x3 −2x4 = −2,
x1
10.21. а)		+ 2x2		+ x3 = −17,
4x1
	−3x3 + x4 =1,
x1
x1 + x2 + x4 = −3,
		+3x2		+7x4 = 3,
б) 3x1
4x1 −2x2 +6x3 + 4x4 = 3,
		+ 4x2		−2x3 +7x4 = 4,
2x1
x1 + 2x2 − x3 −3x4 = 4,
	+5x2 − x3 + 4x4 = 3,
x1
в)		+7x2		−2x3 + 2x4 = −1,
2x1
				+ x3 +3x4 =1.
− x1 +3x2
x1 + 2x2 + 4x3 +3x4 = 5,
		+3x2		+ x3 + 2x4 = 4,
10.22. а) 3x1
3x1 + 2x2 + 2x3 +7x4 = 5,

−2x1 + x2 +7x3 + 4x4 = 5,
4x1 +5x2 + 2x3 = 3,
	−2x2 −4x4 =1,
x1
б)		+5x2		+ 2x3 = 2,
5x1
		+3x2		+ x3 + x4 =1,
2x1
2x1 − x2 + x3 −3x4 = 4,
	+ 4x2 −4x3 +5x4 = −1,
x1
в)		+ x2 − x3 +3x4 =1,
3x1
5x	1	−2x	2	+ 2x	3	−3x	4	= 2.

x1 − x2 +3x3 + 2x4 = 3,

10.23. а) 3x1 + 2x2 + x3 +5x4 =10,3x1 + x2 − x3 −2x4 = −1,

2x1 +5x2 + 2x3 − x4 = −7,x1 + 2x2 + x3 +3x4 = −1,

5x1 + 4x2 + 2x3 +3x4 = −2, б) 5x1 +5x2 + 2x3 + 2x4 = 0,

2x1 + 2x2 + x3 + 2x4 = −1,x1 −7x2 +3x3 + x4 = 5,

в) 2x1 +3x2 −3x4 = 9,3x1 + x2 − x3 + x4 = 3,

2x1 + 2x2 −3x3 + 4x4 = 7.x1 + 4x2 −2x3 −3x4 = 23,

10.24. а) 3x1 + 2x2 + 2x4 = 27,

5x1 +8x2 +8x3 +6x4 = 43,2x1 + 4x2 +7x3 +3x4 =12,x1 + x2 +3x3 −2x4 = 7,

б) 4x1 + x2 −3x3 + x4 = −2,2x1 + x2 + x3 − x4 = 4,

3x1 + x2 − x3 =1,

x1 −2x2 − x3 +5x4 =10,

в) 4x1 −5x2 + 2x3 −3x4 = 2,3x1 −4x2 + x3 + 2x4 = 5,6x1 −7x2 + 4x3 + 2x4 = −3.

39										40
− x1 +8x2 + x3 +3x4 = 30,
		+5x2 − x3 + 4x4 = 50,
10.25. а) 8x1
x1 +7x2 + x4 = 32,
		+3x2 + x4 =19,
2x1
x1 − x2 +3x3 +3x4 = 2,
		− x2 + 4x3 −5x4 =1,
2x1
б)		+ x2 + 2x3 − x4 = −7,
4x1
5x	1	−3x	2	+11x	3		+ 4x	4		= 4,

x1 +3x2 −2x3 +5x4 =1,
		+ x2 −2x3 + x4 =1,
в) 3x1
2x1 − x2 +7x3 −3x4 = 2,
		−5x2 +9x3 −10x4 = 2.
2x1
3x1 + 2x2 − x3 +3x4 = 3,
		− x2 + x3 −2x4 = 9,
4x1
10.26. а)		−4x2 −3x3 − x4 =15,
2x1
	−3x2 + x3 −3x4 =11,
x1
2x1 + 4x2 −2x3 +7x4 = 4,
	− x2 + 2x3 = −1,
x1
б)		+ x2 + 2x3 + 2x4 = −7,
3x1
6x	1	−4x	2	+10x		3	+ 4x		4	=1,

3x1 + 2x2 −2x3 +7x4 =1,

в) −3x1 −2x2 + 2x3 +3x4 = 5,2x1 + x2 − x3 +5x4 = −1,

3x1 + x2 − x3 −2x4 = −4.

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