Типовой_2_2011_24 вар

	2x −2x −3x −7x +2x = 0
		1	2	3		4		5
14)	x1	+11x2 +34x4 −5x5 = 0							,
	x	−5x	−2x		−16x	4	+3x		= 0
	1	2	3				5

x1 +3x2 −5x3 +9x4 − x5 = 0

15)2x1 +7x2 −3x3 −7x4 +2x5 = 0,x1 +4x2 +2x3 −16x4 +3x5 = 0

x1 − x2 + x3 −2x4 + x5 = 0

16)x1 + x2 −2x3 − x4 +2x5 = 0,x1 −3x2 +4x3 −3x4 = 0

	3x +x		−8x +2x +x =0
		1 2	3		4 5
17)	x1	+11x2 −12x3 −5x5 =0 ,
	x	−5x	+2x	+x	+3x =0
	1	2	3	4	5

2x +2x −2x + x −3x = 0

18)3x1 − x2 +2x3 − x4 +2x5 = 0 ,x1 −3x2 +4x3 −2x4 +5x5 = 0

2x1 + x2 − x3 +7x4 +5x5 = 0

19)x1 −2x2 +3x3 −5x4 −7x5 = 0 ,3x1 − x2 +2x3 +2x4 −2x5 = 0

x1 +2x2 +3x3 + x4 − x5 = 0

20)2x1 −2x2 −6x3 −4x4 + x5 = 0,

3x1 −2x2 +3x3 +3x4 = 03 42 51

2x +3x +4x +7x =1
		1		2			3		4
x1		+ x2 −3x3 −4x4 =1 ;
4x +5x −2x − x									=3
		1		2			3		4
x		+4x		−3x			− x		= 2
	1		2		3		4
2x1 +7x2 −4x3 −3x4 =3;
x		+2x		+ x		−3x		4	= 0
	1		2	3
2x			− x	+ x		+ x =1
		1	2	3			4
x1		+2x2 − x3 +4x4 = 2 ;
x		+7x		−4x			+11x =5
	1		2			3			4
x +7x +9x +4x =2
	1		2	3			4
2x1 +2x2 +3x3 +5x4 =4 ;
				+5x3 +12x4 =10
5x1 +3x2
x −3x + x +2x = 4
	1		2	3				4
2x1 −5x2 +4x3 +3x4 = 7;
x		−2x		+3x			+ x	4	=3
	1		2		3
x +2x −3x −4x =1
	1		2		3			4
3x1 +7x2 −2x3 − x4 = 4;
2x			+5x + x				+3x		=3
		1		2		3		4
x		+3x		− x		−2x			=1
	1		2	3			4
2x1 +7x2 −4x3 −3x4 =3;
x		+4x		−3x			− x		= 2
	1		2		3		4

	7x −14x +3x − x + x = 0
		1			2			3	4			5
21)	x1	−2x2 + x3 −3x4 +7x5 = 0 ,
	5x1 −10x2 + x3 +5x4 −13x5 = 0
	x	+ x	2	+ x − x					− x		= 0
	1					3		4	5
22)	2x1 + x2 −2x3 − x4 −2x5 = 0,
	x	+2x		2	+5x			−2x		− x			=	0
	1						3		4		5
	7x +2x				2	− x		−2x		+2x			= 0
		1					3		4			5
23)	x1	−3x2 + x3 − x4 − x5 = 0												,
	2x +3x					+	2x + x			+ x			=	0
		1		2				3	4		5
	2x −2x −3x −7x +2x = 0
		1			2			3		4			5
24)	x1	+11x2 +34x4 −5x5 = 0												,
	x	−5x			−2x			−	16x		+3x			= 0
	1		2				3		4				5

x1 − x2 +4x3 +3x4 = 0

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

x1 −3x2 +4x3 +3x4 = 2

3x1 −8x2 + x3 +2x4 =5 ;2x1 −5x2 −3x3 − x4 =3

x1 +4x2 −2x3 −3x4 = 2

2x1 +9x2 − x3 −4x4 =5;x1 +5x2 + x3 − x4 =3

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

ЗАДАЧА 12. Найдите общее решение данной однородной системы уравнений, построив ее фундаменальную систему решений.

	x1 −2x2 +3x3 −4x4 = 0
	2x		−4x +				5x +	7x =		0
1)		1		2			3	4
		6x	−12x			+17x		−9x		= 0
		1		2			3		4
	7x		−14x			+18x		+17x			= 0
		1		2			3		4
	2x1 +3x2 − x3 −5x4 = 0
	4x +6x +						2x − x =		0
3)		1		2			3	4
		2x	+3x		−5x −14x				= 0
		1		2			3	4
	10x			+15x			+3x	−7x		= 0
		1			2		3	4

	x		−2x		+x +x −x =				0
		1		2	3	4		5
2) 2x1 +x2 −x3 −x4 +x5 =0
		x	+8x		−5x	−5x		+5x =0
		1		2	3	4			5
	3x			−x	−2x	+x	−x =0
			1	2	3	4		5
	x		+4x		+2x	−3x		=0
		1		2	3	5
4)	2x1 +9x2 +5x3 +2x4 +x5 =0
	x		+3x		+x −2x		−9x		=0
		1		2	3	4		5

	3x +4x +3x +2x = 0									3x1 +2x2 +x3 +3x4 +5x5 =0
		1	2		3	4
	5x1 +7x2 +4x3 +3x4 = 0
5)	4x +5x +5x +3x = 0								6)	6x1		+4x2	+3x3 +5x4 +7x5 =0
		1	2		3	4						+6x2	+5x3 +7x4 +9x5 =0
	5x +6x +7x +4x = 0									9x1
		1	2		3	4
	x +2x +4x −3x = 0									x −2x +x −x +x =0
	1		2		3	4					1	2	3	4	5
7) 3x1 +5x2 +6x3 −4x4 = 0									8) 2x1 +x2 −x3 +2x4 −3x5 =0
	4x1 +5x2 −2x3 +3x4 = 0									3x1 −2x2 −x3 +x4 −2x5 =0
	3x +8x +24x −19x = 0									2x		−5x	+x	−2x	+2x =0
		1	2		3		4				1	2	3	4	5
	3x1 +4x2 −5x3 +7x4 = 0										x1 +x2 +x3 +2x4 +x5 =0
	2x −3x +3x −2x = 0
		1	2		3	4
9)	4x +11x			−13x		+16x = 0			10)		x1	−2x2	−3x3 +x4 −x5 =0
		1	2		3		4						−2x3 +3x4 =0
	7x −2x + x +3x = 0										2x1 −x2
		1	2		3	4
	2x +3x −x				+5x	+x	=0		3x +3x +5x +7x +4x =0
		1	2	3	4	5					1	2	3	4	5
11) 3x1 +x2 +2x3 −7x4 +x5 =0								12) 2x1 +2x2 +3x3 +5x4 +3x5 =0
	4x1 −x2 +6x3 −14x4 +3x5 =0								4x1 +4x2 +7x3 +9x4 +5x5 =0
	x −2x +4x −7x +2x =0								5x +5x +9x +11x +6x =0
		1	2	3	4		5				1	2	3	4	5
	3x +5x +2x +4x = 0								x +x −2x +3x −3x =0
		1	2		3		4			1		2	3	4	5
13) 5x1 +4x2 +3x3 +5x4 = 0								14) 2x1 +2x2 +3x3 −x4 −20x5 =0
	9x1 +2x2 +5x3 +7x4 = 0								4x2 +x3 −x4 +2x5 =0
	5x −9x +2x = 0								x +2x −4x +5x +2x =0
		1	2		3					1		2	3	4	5

2x +x +4x +x =0										2x −2x +3x +6x +5x =0
	1		2				3		4	1	2			3	4			5
15) 3x1 +2x2 −x3 −6x4 =0										16) −4x1 +5x2 −7x3 −3x4 +8x5 =0
7x1 +4x2 +6x3 −7x4 =0										−6x1 +7x2 −10x3 −9x4 +3x5 =0
x	+8x			+	7x			=0		8x	−9x		+13x		+15x			+2x =0
1		3				4				1	2			3		4		5
2x −5x +4x +3x =0										3x +6x +10x +4x −2x =0
	1			2				3	4		1	2			3		4	5
17) 3x1 −4x2 +7x3 +5x4 =0										18) 6x1 +10x2 +17x3 +7x4 −3x5 =0
4x1 −9x2 +8x3 +5x4 =0										9x1 +3x2 +2x4 +3x5 =0
−3x +			2x			−	5x		+3x =0	12x −2x				+x	+8x		+5x =0
		1		2				3	4		1		2	3	4			5
2x1 −4x2 +5x3 +3x4 =0										x +2x +3x +2x −6x =0
										1	2			3	4			5
										2x1 +3x2 +7x3 +6x4 −18x5 =0
19) 3x1 −6x2 +4x3 +2x4 =0										20)
		−8x2 +17x3 +11x4 =0								3x1 +5x2 +11x3 +9x4 −27x5 =0
4x1										x	+4x		+	5x +2x		−		6x =0
										1	2			3	4			5
3x +5x +2x +4x = 0										x +x −2x +3x −3x =0
	1			2				3	4	1	2			3	4			5
21) 5x1 +4x2 +3x3 +5x4 = 0										22) 2x1 +2x2 +3x3 −x4 −20x5 =0
9x1 +2x2 +5x3 +7x4 = 0										4x2 +x3 −x4 +2x5 =0
5x		−9x				+	2x		= 0	x	+2x		−4x		+5x		+2x =0
	1			2				3		1	2			3	4			5
2x +x +4x +x =0										2x −2x +3x +6x +5x =0
	1		2				3		4	1	2			3	4			5
23) 3x1 +2x2 −x3 −6x4 =0										24) −4x1 +5x2 −7x3 −3x4 +8x5 =0
7x1 +4x2 +6x3 −7x4 =0										−6x1 +7x2 −10x3 −9x4 +3x5 =0
x	+8x			+	7x			=0		8x	−9x		+13x		+15x			+2x =0
1		3				4				1	2			3		4		5