Тапсырма 3. Берілген векторлар жүйесінің рангін және базисін табыңдар:
1) a1 = (4, 1, 0, 3), a2 = (5, 2, 6, 2), a3 = (5, 1, 4, 3), a4 = (2, 1, 7, –1), a5 = (–1, 4, –2, 7);
2) a1 = (5, 4, 0, 6), a2 = (4, 5, –1, 3), a3 = (–1, 4, 3, 1), a4 = (5, 1, 4, 5), a5 = (1, 3, 7, –2);
3) a1 = (1, 2, 7, –2), a2 = (1, 0, 7, 1), a3 = (5, 5, 3, 7), a4 = (7, –2, –1, 3), a5 = (3, –1, 4, –2);
4) a1 = (3, 7, 2, 5), a2 = (7, 3, 5, 6), a3 = (4, 7, 0, 7), a4 = (0, 2, 1, –1), a5 = (1, –1, –2, 7);
5) a1 = (3, 6, 2, 5), a2 = (6, –2, 6, 3), a3 = (7, –1, 2, 1), a4 = (–2, 3, 0, 7), a5 = (3, 2, 5, 6);
6) a1 = (0, 7, 3, 0), a2 = (5, 7, –2, 1), a3 = (3, 5, 2, 5), a4 = (–1, 3, 6, 4), a5 = (2, 0, 7, 1);
7) a1 = (6, 5, 3, 2), a2 = (–2, –1, –1, –1), a3 = (0, 0, 3, 1), a4 = (7, 5, –2, –1), a5 = (–2, 5, 7, 3);
8) a1 = (1, 3, 4, 6), a2 = (1, 1, –1, 2), a3 = (5, 1, 3, 0), a4 = (4, 1, –1, 1), a5 = (6, 5, 7, 5);
9) a1 = (–2, 2, 0, 6), a2 = (3, –2, –2, 2), a3 = (–1, 1, 0, 1), a4 = (7, 6, –1, 4), a5 = (2, –2, 2, 1);
10) a1 = (7, 1, 3, –1), a2 = (–2, 7, –2, –2), a3 = (7, –1, –2, 4), a4 = (1, 2, 3, 0), a5 = (7, 5, 6, 7);
11) a1 = (7, 5, 4, 5), a2 = (–1, 3, 7, 7), a3 = (4, –2, 7, 3), a4 = (–1, 2, 1, –1), a5 = (7, 6, –1, 6);
12) a1 = (3, –1, 3, 0), a2 = (3, 1, 1, –2), a3 = (7, 7, –2, 1), a4 = (6, –1, 1, 5), a5 = (7, 2, 5, –2);
13) a1 = (7, –2, 2, 3), a2 = (1, 0, 2, –2), a3 = (4, 7, 0, –2), a4 = (2, 6, 0, 7), a5 = (5, 5, 1, 2);
14) a1 = (3, 7, 4, –1), a2 = (3, 2, 3, 2), a3 = (1, –2, 7, 2), a4 = (–1, 3, 7, 3), a5 = (7, 1, 0, 3);
15) a1 = (4, 4, –2, –2), a2 = (6, 2, 5, 6), a3 = (7, 5, –1, 0), a4 = (5, 0, 1, 4), a5 = (7, –1, 2, –1);
16) a1 = (2, 1, 3, 7), a2 = (6, –1, 0, 2), a3 = (–1, 3, 4, –1), a4 = (6, 5, –1, 2), a5 = (4, 5, –2, 0);
17) a1 = (6, 5, 1, 6), a2 = (3, 5, 1, –1), a3 = (0, –2, 0, –1), a4 = (–1, 2, 1, 5), a5 = (1, 0, –1, 4);
18) a1 = (–1, 1, 4, 0), a2 = (1, 4, 0, 6), a3 = (1, 0, –2, 5), a4 = (6, 7, 1, –1), a5 = (–2, 3, 7, 5);
19) a1 = (–2, 1, 5, 6), a2 = (7, 6, 4, 4), a3 = (6, 3, 2, 0), a4 = (3, 6, 1, 0), a5 = (3, –2, 3, –2);
20) a1 = (4, 0, –1, 2), a2 = (3, 4, 3, 6), a3 = (2, 4, 4, 1), a4 = (0, 7, –1, 7), a5 = (6, –1, 4, 3);
21) a1 = (2, 1, 3, 5), a2 = (2, 5, –2, –2), a3 = (0, 2, 5, 7), a4 = (–1, 5, 3, 5), a5 = (5, 7, 1, –2);
22) a1 = (5, 6, –2, 4), a2 = (6, 0, –2, –2), a3 = (–1, 0, –2, 5), a4 = (5, 1, –1, 3), a5 = (3,–2, 0, 6);
23) a1 = (2, 2, 7, 2), a2 = (6, 2, –2, 2), a3 = (4, 1, 6, 4), a4 = (1, 4, 7, 3), a5 = (1, 6, 3, 7);
24) a1 = (7, –1, –1, 7), a2 = (2, 6, 3, 3), a3 = (0, 4, 2, 1), a4 = (2, 2, 3, 4), a5 = (1, 6, –1, 3);
25) a1 = (6, 5, 1, –2), a2 = (1, 0, 1, 1), a3 = (2, –1, 7, 2), a4 = (–2, 1, –1, –1), a5 = (6, 1, 0, –1);
26) a1 = (–2, –2, 4, 0), a2 = (–2, –1, 4, 5), a3 = (5, –1, –2, 4), a4 = (5, 4, 7, 1), a5 = (0, 4, 1, 2);
27) a1 = (–1, 5, 0, 5), a2 = (1, 0, 6, 5), a3 = (–2, 0, 2, 2), a4 = (4, 6, 4, 0), a5 = (7, 6, 1, –1);
28) a1 = (5, 1, 4, 3), a2 = (6, 7, 2, –2), a3 = (0, 1, 1, 0), a4 = (7, –2, 4, 5), a5 = (3, 7, 2, 4);
29) a1 = (–1, 7, 2, –1), a2 = (3, 4, 6, 3), a3 = (2, –1, 3, –1), a4 = (2, –1, 1, 2), a5 = (0, 7, 7, 3);
30) a1 = (6, –2, 5, 5), a2 = (0, 5, –2, 6), a3 = (–2, –2, 1, 6), a4 = (6, 7, 0, 4), a5 = (3, 5, 1, 4);
31) a1 = (–1, 1, 1, 1), a2 = (5, 6, 1, 6), a3 = (4, 5, 0, 5), a4 = (2, 4, 1, 6), a5 = (–2, 7, 1, 0);
32) a1 = (2, 0, –1, 7), a2 = (4, 3, –2, 5), a3 = (1, –1, 5, 2), a4 = (5, 0, 2, 1), a5 = (5, 3, 3, 5);
33) a1 = (7, 2, –1, 7), a2 = (4, 1, 6, 2), a3 = (3, 1, 0, 2), a4 = (0, 6, 0, 4), a5 = (6, 0, 6, –2);
34) a1 = (4, 4, 5, 0), a2 = (1, 5, 6, 6), a3 = (3, 1, 2, 1), a4 = (4, 1, 1, 1), a5 = (7, 2, 1, 0);
35) a1 = (1, 0, 6, –2), a2 = (0, 4, 6, 0), a3 = (5, 0, 2, 5), a4 = (1, 5, –1, 4), a5 = (3, 6, 7, 6);
36) a1 = (2, 5, 1, 1), a2 = (6, 0, 1, 4), a3 = (6, 3, –2, 4), a4 = (–2, –1, 0, 4), a5 = (5, 4, 5, 1);
37) a1 = (0, 7, 4, 2), a2 = (1, 3, 7, 2), a3 = (6, 2, 4, –1), a4 = (0, –2, –2, 4), a5 = (6, 3, 6, –2);
38) a1 = (–1, 3, –1, –1), a2 = (–2, 1, 3, 7), a3 = (7, –2, 1, 5), a4 = (–2, 4, 0, 3), a5 = (2, 0, 2, 0);
39) a1 = (0, 0, –1, 7), a2 = (4, 1, 7, 4), a3 = (2, –2, –1, 4), a4 = (2, 3, 1, –2), a5 = (2, 0, 7, 7);
40) a1 = (–1, –1, 6, 6), a2 = (5, 4, 7, –1), a3 = (5, 0, 6, 2), a4 = (0, 1, 0, 1), a5 = (4, 3, 3, –1);
Тапсырма 4. Теңдеулер жүйесін шешiңдер:
1)
3x1 – x2 + x3 – x4 = 4
4x1 – x3 + 2x4 = 1
x1 + 2x2 – x3 + 5x4 = –1
3x1 + 2x2 + x3 = 8
2)
6x1 + x2 + x3 + x4 = 6
2 x1 – x2 – x3 + x4 = –6
6x2 – x3 + 5x4 = 19
–x1 – x2 + 2x3 + 2x4 = 8
3)
2x1 + 3x2 – x3 – x4 = 6
x1 + x3 + x4 = 0
3x1 – x2 + 4 x3 = 2
4x1 + x2 – x3 – x4 = 10
4)
x1 – x2 + x3 – x4 = 0
2x1 – x2 + 2x3 – x4 = 2
4x1 – x2 + 2x3 – x4 = 9
3x1 + x2 – 3x3 + x4 = 2
5)
2x1 – 4x2 + 5x3 – 6x4 = –25
x1 + x3 + x3 + x4 = 5
3x1 – x2 – x3 = 7
x1 – 2 x2 + 4 x3 – 4 x4 = –18
6)
2x1 + 2x2 – x3 – x4 = 7
3 x1 – x3 + 2 x4 = 0
6x1 – 5x2 – 4x3 + 3x4 = –1
x1 – x2 – x3 + x4 = –1
7)
3x1 – x2 + 4x3 – x4 = –1
2 x1 + 2 x2 + x3 = 16
x1 + x2 + x3 + x4 = –3
3x1 + x2 + 6x2 + 4x3 = 16
8)
3x1 – x2 – x3 – x4 = 3
2 x1 + 2 x2 – 2 x3 – 3 x4 = 23
x1 – x2 – x3 + x4 = –2
5x1 + 4x2 – 3x3 – 2x4 = 34
9)
2x1 – x2 – x3 = –3
x1 + x2 + x3 + x4 = 6
4x1 – x2 – 6x3 – x4 = –31
6x1 + 10x2 – x3 – x4 = –10
10)
x1 + 2 x2 – x3 + x4 = 2
4x1 – x2 – x4 = 7
2x1 + x2 – x3 – x4 = –3
5x1 – x3 + 2x4 = 0
11)
2x1 + 4x2 + 6x3 + x4 = 19
5 x2 – 6 x3 – 2 x4 = 19
–x1 – x2 + 4x3 + 6x4 = –7
x1 + x2 – x3 – x4 = 9
12)
3 x1 + 6 x2 + x4 = 7
x1 + x2 + x3 + x4 = 6
2x1 + 3x2 – x3 – 6x4 = –21
2x1 + 2x2 – 2x3 + 5x4 = 24
13)
5 x1 + 6 x2 – 4 x3 – 4 x4 = –20
x1 + x2 + x3 + x4 = 7
–2x1 – 3x2 + x3 + x4 = 5
6x1 – 2x2 – 4x3 – 5x4 = –12
14)
6 x1 + 5 x2 – x4 = 0
x1 + x2 + x3 + x4 = 5
2x1 + 3x2 + 4x3 – 5x4 = 10
–3x1 – 4x2 + 4x3 + 3x4 = 20
15)
2 x1 + x2 – x3 – x4 = 0
x1 + x2 + x3 = –1
6x1 + 5x2 + 4x3 + x4 = 2
2x1 – x2 – x3 – x4 = 6
16)
2 x1 + 4 x2 + 6 x3 + x4 = 19
5x2 – 6x3 – 2x4 = 19
–x1 – x2 + 4x3 + 6x4 = –7
x1 + x2 – x3 – x4 = 9
17)
2 x1 – 2 x2 – x3 – x4 = 1
4x1 + 6x2 + x4 = –1
x1 – x2 – x3 + x4 = 1
5x1 – 3x2 + x3 – x3 = 9
18)
–x1 – x2 + 2x3 + 2x4 = 4
6 x1 + 5 x3 – x3 – x4 = 0
–3x1 – 3x2 + 4x3 = 4
6x1 – x2 + 5x3 + 4x4 = 23
19)
6 x1 + 5 x2 – x3 – x4 = –6
3x1 + 4x2 – x3 = 0
2x1 + 2x2 + x3 + x4 = 13
–x1 – x2 – x3 + 2x4 = 9
20)
2x1 + 2x2 – x3 – x4 = 0
6 x1 + 5 x2 + x4 = –1
3x1 + x3 + 2x4 = 3
4x1 + x2 – x3 – x4 = 6
21)
6 x1 + 3 x2 + 2 x3 – x4 = 5
x1 + x2 – x3 = 9
2x1 + 6x2 – 4x3 – 3x4 = 27
5x1 + 7x2 + x4 = –18
22)
x1 + x2 + x3 – x4 = 11
x1 + x4 – 3 x3 – x4 = –11
x2 + x3 – 8 x4 = –1
2x1 – 3x2 + x3 + x4 = 2
23)
x1 – x2 + x3 – x4 = 2
2x1 – x2 + 2x3 – 2x4 = 6
6x2 + 4x3 – 5x4 = 16
3x1 + 2x2 – x3 – x4 = 21
24)
2x1 + x2 + x3 + x4 = 2
x1 – x2 – x4 = 2
3x1 + 2x2 – 4x3 = –1
4x1 + 6x2 + 7x3 + 6x4 = 12
25)
6 x1 – 5 x2 – 4 x3 + 4 x4 = 2
x1 + x2 + x3 + x4 = 2
4x1 – x2 –x4 = 7
3x1 – x3 + 5x4 = 12
26)
2 x1 + x2 + x3 – x4 = 4
x1 + x2 + x3 – x4 = 2
3x1 + 2x2 – 3x4 = 0
x2 – x3 – x4 = –2
27)
2 x1 + 4 x3 – 5 x4 = –9
x1 + x2 – x3 – x4 = –3
x1 + x2 + x3 + 2 x4 = 12
6x1 + 5x2 – 2x3 – x4 = 16
28)
6x1 + 2x2 – 4x3 = –16
x1 + x2 – x3 + 4 x4 = 31
2x1 + 3x2 – 5x4 = –17
6x1 + 7x2 – 4x3 = 19
29)
6 x1 + 7 x2 – 4 x3 + x4 = –7
3x1 + 4x3 – 7x4 = 19
x1 + x2 + x3 + x4 = 8
2x1 – x2 – x3 + 2x4 = 1
30)
6x1 – 3x2 + 4x3 = 3
x1 + x2 – x3 – x4 = 9
3x1 – 4x2 – x3 + x4 = –10
5x1 + 4x2 – 4x3 + 4x4 = 14
31)
2 x1 – x2 + x3 + 2 x4 + 3 x5 = 2
6x1 – 3x2 + 2x3 + 4x4 + 5x5 = 3
6x1 – 3x2 + 4x3 + 8x4 + 13x5 = 9
4x1 – 2x2 + x3 + x4 + 2x5 = 1
32)
x1 + x2 + 3 x3 – 2 x4 + 3 x5 = 1
2x1 + 2x2 + 4x3 – x4 + 3x5 = 2
3x1 + 3x2 + 5x3 – 2x4 + 3x5 = 1
2x1 + 2x2 + 8x3 – 3x4 + 9x5 = 2
33)
3x1 + 2x2 + 2x3 + 2x4 = 2
2 x1 + 3 x2 + 2 x3 + 5 x4 = 3
9x1 + x2 + 4x3 – 5x4 = 1
2x1 + 2x2 + 3x3 + 4x4 = 5
7x1 + x2 + 6x3 – x4 = 7
34)
9x1 – 3x2 + 5x3 + 6x4 = 4
6 x1 – 2 x2 + 3 x3 + x4 = 5
3x1 – x2 + 3x3 + 14x4 = –8
35)
2x1 – x2 + 3x3 – 7x4 = 5
6 x1 – 3 x2 + x3 – 4 x4 = 7
4x1 – 2 x2 + 14 x3 – 31 x4 = 18
36)
3 x1 – 2 x2 + 5 x3 + 4 x4 = 2
6x1 – 4x2 + 4x3 + 3x4 = 3
9x1 – 6x2 + 3x3 + 2x4 = 4
37)
2 x1 + 5 x2 – 8 x3 = 8
4x1 + 3x2 – 9x3 = 9
2x1 + 3x2 – 5x3 = 7
x1 + 8x2 – 7x3 = 12
38)
3 x1 + 4 x2 + x3 + 2 x4 = 3
6x1 + 8x2 + 2x3 + 5x4 = 7
9x1 + 12x2 + 3x3 + 10x4 = 13
39)
3 x1 – 5 x2 + 2 x3 + 4 x4 = 2
7x1 – 4x2 + x3 + 3x4 = 5
5x1 + 7x2 – 4x3 – 6x4 = 3
Тапсырма 5. Теңдеулер жүйесін шешіңдер:
1)
24x1 + 14x2 + 30x3 + 40x4 + 41x5 = 28
36x1 + 21x2 + 45x3 + 61x4 + 62x5 = 43
48x1 + 28x2 + 60x3 + 82x4 + 83x5 = 58
60x1 + 35x2 + 75x3 + 99x4 + 102x5 = 69
2)
10x1 + 23x2 + 17x3 + 44x4 = 25
15 x1 + 35 x2 + 26 x3 + 69 x4 = 40
25x1 + 57x2 + 42x3 + 108x4 = 65
30x1 + 69x2 + 51x3 + 133x4 = 95
3)
12x1 + 14x2 – 15x3 + 23x4 + 27x5 = 5
16 x1 + 18 x2 – 22 x3 + 29 x4 + 37 x5 = 8
18x1 + 20x2 – 21x3 + 32x4 + 41x5 = 9
10x1 + 12x2 – 16x3 + 20x4 + 23x5 = 4
4)
x1 + 2x2 + 3x3 + x4 = 3
x1 + 4 x2 + 5 x3 + 2 x4 = 2
2x1 + 9x2 + 8x3 + 3x4 = 7
3x1 + 7x2 + 7x3 + 2x4 = 12
5x1 + 7x2 + 9x3 + 2x4 = 20
5)
2x1 + 3x2 + x3 + 2x4 = 4
4 x1 + 3 x2 + x3 + x4 = 5
5x1 + 11x2 + 3x3 + 2x4 = 2
2x1 + 5x2 + x3 + x4 = 1
x1 – 7x2 – x3 + 2x4 = 7
6)
8x1 + 6x2 + 5x3 + 2x4 = 21
3 x1 + 3 x2 + 2 x3 + x4 = 10
4x1 + 2x2 + 3x3 + x4 = 8
3x1 + 5x2 + x3 + x4 = 15
7x1 + 4x2 + 5x3 + 2x4 = 18
7)
6x1 + 3x2 + 2x3 + 3x4 + 4x5 = 5
4 x1 + 2 x2 + x3 + 2 x4 + 3 x5 = 4
4x1 + 2x2 + 3x3 + 2x4 + x5 = 0
2x1 + x2 + 7x3 + 3x4 + 2x5 = 1
8)
x1 + 2x2 + 3x3 – 2x4 + x5 = 4
3x1 + 6x2 + 5x3 – 4x4 + 3x5 = 5
x1 + 2x2 + 7x3 – 4x4 + x5 = 11
2x1 + 4x2 + 2x3 – 3x4 + 3x5 = 6
9)
6x1 + 4x2 + 5x3 + 2x4 + 3x5 = 1
3 x1 + 2 x2 + 4 x3 + x4 + 2 x5 = 3
3x1 + 2x2 – 2x3 + x4 = –7
9x1 + 6x2 + x3 + 3x4 + 2x5 = 2
10)
3 x1 + 2 x2 + 5 x3 + 2 x4 + 2 x5 = 1
2x1 + x2 + 4x3 + 4x4 + x5 = 3
x2 – 2 x3 + x4 = –7
2x1 + 3x2 + x3 + 3x4 + 3x5 = 2
11)
x1 + x2 + x3 + x4 + x5 = 1
x1 + 2x2 + 3x3 + 4x4 + 5x5 = 2
2x1 + 4x2 + 10x3 + 15x4 + 20x5 = 16
x1 – 8 x2 + 6 x3 + 6 x4 + x5 = 56
3x2 + 4x3 + 2x4 + 3x5 = 6
12)
4x1 – 4x2 + 3x3 + 6x4 + 8x5 = 5
2 x1 – 2 x2 + x3 + 2 x4 + 2 x5 = 1
x1 – x2 + x3 + 2 x4 + 3 x5 = 2
x1 – x2 + 3 x3 + 7 x4 + 11 x5 = 8
13)
x1 + x2 + 3 x3 – 2 x4 + x5 = 4
3x1 + 3x2 + 5x3 – 4x4 + 3x5 = 5
x1 + x2 + 7 x3 – 4 x4 + x5 = 11
2x1 + 2x2 + 2x3 – 3x4 + 3x5 = 6
14)
x1 + 2x2 + 3x3 + x4 + 2x5 = 4
x1 + 2x2 – x5 = 1
2x1 + 2x2 + 5x3 + x4 + x5 = 1
2x1 + 3x2 + 6x3 + 2x4 + x5 = 1
3x1 + x2 – 7x3 – 2x4 + 2x5 = 7
15)
2x1 + 5x2 + 3x3 + 3x4 + x5 = 11
3 x1 + 4 x2 + 4 x3 + 2 x4 + x5 = 13
4x1 + 5x2 + x3 = 3
5x1 + x2 + 2x3 = 3
6x1 + 7x2 + 7x3 + x4 + 2x5 = 23
16)
2x1 + 5x2 + 3x3 + 3x4 + x5 = 11
3 x1 + 4 x2 + 4 x3 + 2 x4 + x5 = 13
4x1 + 5x2 + x3 = 3
5x1 + x2 + 2x3 = 3
6x1 + 7x2 + 7x3 + x4 + 2x5 = 23
17)
6x1 + 2x2 + 3x3 = 5
3 x1 + 2 x2 + 6 x3 + x4 = 1
x2 + 6 x3 + 2 x4 + x5 = –1
3x3 + 2x4 + 2x5 = 1
3x1 + x2 + x4 + x5 = 0
18)
2 x1 – 3 x2 + 5 x3 + 7 x4 = 1
4x1 – 6x2 + 2x3 + 3x4 = 2
2x1 – 3x2 – 11x3 – 15x4 = 1
19)
2 x1 + 7 x2 + 3 x3 + x4 = 6
3x1 + 5x2 + 2x3 + 2x4 = 4
9x1 + 4x2 + x3 + 7x4 = 2
20)
12 x2 – 16 x3 + 25 x4 = 29
27x1 + 24x2 – 32x3 + 47x4 = 55
50x1 + 51x2 – 68x3 + 95x4 = 115
31x1+21x2–28x3+ 46x4= 50
21)
45x1 – 28x2 + 34x3 – 52x4 = 9
36 x1 – 23 x2 + 29 x3 – 43 x4 = 3
35x1 – 21x2 + 28x3 – 45x4 = 16
47x1 – 32x2 + 36x3 – 48x4 = –17
27x1 – 19x2 + 22x3 – 35x4 = 115
Тапсырма 6. параметріне тәуелді сызықтық теңдеулер жүйесін зерттеп, шешіңдер:
1)
5x1 – 3x2 + 2x3 + 4x4 = 3
4x1 – 2x2 + 3x3 + 7x4 = 1
8x1 – 6x2 – x3 – 5x4 = 9
7x1 – 3x2 + 7x3 + 17x4 =
2)
3x1 + 2x2 + 5x3 + 4x4 = 3
2 x1 + 3 x2 + 6 x3 + 8 x4 = 5
x1 – 6 x2 – 9 x3 – 20 x4 = –11
4x1 + x2 + 4x3 + x4 = 2
3)
2x1 + 5x2 + x3 + 3x4 = 2
4 x1 + 6 x2 + 3 x3 + 5 x4 = 4
4x1 + 14x2 + x3 + 7x4 = 4
2x1 – 3x2 + 3x3 + x4 = 7
4)
2x1 – x2 + 3x3 + 4x4 = 5
4 x1 – 2 x2 + 5 x3 + 6 x4 = 7
6x1 – 3x2 + 7x3 + 8x4 = 9
x1 – 4x2 + 9x3 + 10x4 = 11
5)
2x1 + 3x2 + x3 + 2x4 = 3
4 x1 + 6 x2 + 3 x3 + 4 x4 = 5
6x1 + 9x2 + 5x3 + 6x4 = 7
8x1 + 12x2 + 7x3 + x4 = 9
6)
x1 + x2 + x3 + x4 = 1
x1 + x2 + x3 + x4 = 1
x1 + x2 + x3 + x4 = 1
x1 + x2 + x3 + x4 = 1
7)
(1 + )x1 + x2 + x3 = 1
x1 + (1 + ) x2 + x3 =
x1 + x2 + (1 + ) x3 = 2
8)
( + 1)x1 + x2 + x3 = 2 + 3
x1 + ( + 1) x2 + x3 = 3 + 3 2
x1 + x2 + ( + 1) x3 = 4 + 3 3
9)
x1 + 2x2 + 3x3 = –2
2x1 + 2x2 + 2x3 = 3
5x1 + 6x2 + 7x3 =
10)
2x1 – x2 + x3 = 0
x1 – 2 x2 – 2 x3 = –3
x1 + x2 + 3 x3 = –1
11)
(–1 + 2 ) x1 + x2 + x3 = 2 –
x1 + x2 + x3 = 1
x1 + x2 + x3 = 1
12)
x1 + x2 + x3 + x4 = 1
x1 + x2 + x3 + x4 = –1
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
13)
x1 + 2x2 – x3 = 1
4x1 – x2 + 3x3 = 0
4x1 – x2 + x3 = 0
3x1 + x2 + 4x3 = –1
14)
x1 + x2 + x3 + x4 = 1
x1 + x2 + x3 + x4 = 1
x1 + x2 + x3 + x4 = 1
x1 + x2 + x3 + x4 = 1
15)
2x1 + x2 + 2x3 + 2x4 = 2
2 x1 + 9 x2 + 4 x4 = 2
2x1 + 5x2 + x3 + 3x4 = 2
2x1 – 3x2 + 3x3 + x4 = 7
Тапсырма 7. Біртекті теңдеулер жүйесінің жалпы шешімін және шешімдердің фундаменталдық жүйесін табыңдар:
1)
x1 + 2 x2 + 4 x3 – 3 x4 = 0
3x1 + 5x2 + 6x3 – 4x4 = 0
4x1 + 5x2 – 2x3 + 3x4 = 0
3x1 + 8x2 + 24x3 – 19x4 = 0
2)
2x1 – 4x2 + 5x3 + 3x4 = 0
3 x1 – 6 x2 + 4 x3 + 2 x4 = 0
4x1 – 8x2 + 17x3 + 11x4 = 0
3)
3x1 + 2x2 + x3 + 3x4 + 5x5 = 0
6 x1 + 4 x2 + 3 x3 + 5 x4 + 7 x5 = 0
9x1 + 6x2 + 5x3 + 7x4 + 9x5 = 0
3x1 + 2x2 + 4x3 + 8x5 = 0
4)
3x1 + 5x2 + 2x3 = 0
4 x1 + 7 x2 + 5 x3 = 0
x1 + x2 – 4 x3 = 0
2x1 + 9x2 + 6x3 = 0
5)
6x1 – 2x2 + 2x3 + 5x4 + 7x5 = 0
9 x1 – 3 x2 + 4 x3 + 8 x4 + 9 x5 = 0
6x1 – 2x2 + 6x3 + 7x4 + x5 = 0
3x1 – x2 + 4x3 + 4x4 – x5 = 0
6)
x1 – x3 = 0
x2 – x4 = 0
–x1 + x3 – x5 = 0
–x2 + x4 – x6 = 0
–x3 + x5 = 0
–x4 + x6 = 0
7)
x1 – x3 + x5 = 0
x2 – x4 + x6 = 0
x1 – x2 + x5 – x6 = 0
x2 – x4 + x5 = 0
8)
5x1 + 6x2 – 2x3 + 7x4 + 4x5 = 0
2 x1 + 3 x2 – x3 + 4 x4 + 2 x5 = 0
7x1 + 9x2 – 3x3 + 5x4 + 6x5 = 0
5x1 + 9x2 – 3x3 + x4 + 6x5 = 0
9)
3x1 + 4x2 + x3 + 2x4 + 3x5 = 0
5 x1 + 7 x2 + x3 + 3 x4 + 4 x5 = 0
4x1 + 5x2 + 2x3 + x4 + 5x5 = 0
7x1 + 10x2 + x3 + 6x4 + 5x5 = 0
10)
3 x1 + 2 x2 + 5 x3 + 2 x4 + 7 x5 = 0
3x1 + 4x2 + 7x3 + 4x4 + 5x5 = 0
3x1 + 2x2 – x3 + 2x4 – 11x5 = 0
6x1 + 4x2 + x3 + 4x4 – 13x5 = 0
11)
6x1 – 2x2 + 3x3 + 4x4 + 9x5 = 0
3 x1 – x2 + 2 x3 + 6 x4 + 3 x5 = 0
6x1– 2x2 + 5x3 + 20x4 + 3x5 = 0
9x1– 3x2 + 4x3 + 2x4 + 15x5 = 0
12)
2 x1 + 7 x2 + 4 x3 + 5 x4 + 8 x5 = 0
4x1 + 4x2 + 8x3 + 5x4 + 4x5 = 0
x1 – 9 x2 – 3 x3 – 5 x4 + 4 x5 = 0
3x1 + 5x2 + 7x3 + 5x4 + 6x5 = 0
13)
2x1 + 7x2 + 4x3 – 5x4 + 8x5 = 0
4 x1 + 4 x2 + 8 x3 + 5 x4 + 4 x5 = 0
x1 – 9 x2 + 3 x3 – 5 x4 + 4 x5 = 0
3x1 + 5x2 + 7x3 + 5x4 + 6x5 = 0
Тапсырма 8. Біртекті теңдеулер жүйесінің жалпы шешімін және шешімдердің фундаменталдық жүйесін табыңдар:
1)
3x1 + 4x2 + 3x3 + 9x4 + 6x5 = 0
9x1 + 8x2 + 5x3 + 6x4 + 9x5 = 0
3x1+ 8x2+ 7x3+ 30x4 + 15x5 = 0
6x1 + 6x2 + 4x3 + 7x4 + 5x5 = 0
2)
3x1 + x2 + x3 – 2x4 – 9x5 = 0
9 x1 + 2 x2 + 5 x3 + 2 x4 + x5 = 0
4x1+ x2+ 2x3 – 3x5 = 0
3)
x1 + 4x2 + x3 + 2x4 = 0
6x1 + x2 – 2x3 – 3x4 = 0
5x1 – 6x2 – 4x3 – 7x4 = 0
7x1 + 8x2 + x4 = 0
4)
2x1 – 12x2 – 5x3 – 8x4 – x5 = 0
9 x2 + 3 x3 + 2 x4 + 3 x5 = 0
10x1+ 6x2– 3x3+ 7x4 + 17x5 = 0
6x1+ 3x2 – 2x3 + 4x4 + 10x5 = 0
5)
3x1 + 2x2 + x3 – 6x4 + 2x5 = 0
7 x1+ 3 x2 + 2 x3 – 18 x4 + 6 x5 = 0
11x1+ 5x2+ 3x3– 27x4 + 9x5 = 0
7x1 – 7x2+ 2x3– 48x4+ 16x5 = 0
5x1 + 4x2 + x3 – 6x4 + 2x5 = 0
6)
2x1 + 5x2 + 6x3 + 8x4 = 0
x1 + 2 x2 + 3 x3 + 3 x4 = 0
x1 + 3 x2 + 2 x3 + 4 x4 = 0
x1 + x2 + 5 x3 + 3 x4 = 0
5x1 + 4x2 + 4x3 + 7x4 = 0
7)
5x1 + 3x2 + x3 + 2x4 + 3x5 = 0
7 x1 + 5 x2 + 3 x3 + 4 x4 + 6 x5 = 0
9x1 + 7x2 + 5x3 + 6x4 + 9x5 = 0
8x1 + 4x2 + 2x4 + 3x5 = 0
8)
x1 + x2 + x3 + x4 + x5 = 0
x1 – x2 + 2 x3 – 2 x4 + 3 x5 = 0
x1 + x2 + 4 x3 + 4 x4 + 9 x5 = 0
x1 – x2 + 8 x3 – 8 x4 + 27 x5 = 0
x1+ x2 + 16 x3 + 16 x4 + 81 x5 = 0
9)
x1 + 4x2 + 6x3 + 4x4 + x5 = 0
x1 + x2 + 4 x3 + 6 x4 + 4 x5 = 0
4x1 + x2 + x3 + 4x4 + 6x5 = 0
6x1 + 4x2 + x3 + x4 + 4x5 = 0
4x1 + 6x2 + 4x3 + x4 + x5 = 0
10)
x1 + x2 – 3x4 – x5 = 0
x1 – x2 + 2x3 – x4 = 0
4x1 – 2x2 + 6x3 + 3x4 – 4x5 = 0
2x1 + 4x2 – 2x3 + 4x4 – 7x5 = 0
11)
x1 – 2 x2 + x3 – x4 + x5 = 0
2x1 + x2 – x3 + 2x4 – 3x5 = 0
3x1 – 2x2 – x3 + x4 – 2x5 = 0
2x1 – 5x2 + x3 – 2x4 + 2x5 = 0
12)
x1 – 2x2 + x3 – x4 + x5 = 0
2x1 + x2 – x3 – x4 – 3x5 = 0
x1 + 7 x2 – 5 x3 – 5 x4 + 5 x5 = 0
3x1 – x2 – 2x3 + x4 – x5 = 0
13)
x1 – 2x2 + x3 – x4 + x5 = 0
2x1 + x2 – x3 – x4 + 3x5 = 0
2x1 + 7x2 – 5x3 – 5x4 + 5x5 = 0
3x1 + x2 – 2x3 + x4 – x5 = 0
Тапсырма 9. параметріне тәуелді біртекті сызықтық теңдеулер жүйесін зерттеп, шешіңдер:
1)
x1 + x2 + 3x3 + 4x4 + x5 = 0
x1 + x2 – x3 + x4 + 5 x5 = 0
x1+ x2+ 4x3 + 3x4 – 4x5 = 0
x1 + x2 + 7 x3 + 7 x4 – 3 x5 = 0
2)
2x1 + 2x2 + x3 + x4 = 0
2 x1 + 2 x2 + 2( – 1) x3 + x4 = 0
(2 + 1)x1+ ( + 2)x2+ x3 + x4 = 0
(3 – 2)x1 + 2x2 + x3 + x4 = 0
3)
5x1 – 3x2 + x3 + 4x4 = 0
4 x1 – 2 x2 + 3 x3 + 7 x4 = 0
8x1 – 6x2 – x3 – 5x4 = 0
7x1 – 3x2 + 7x3 + 17x4 = 0
4)
3x1 + 2x2 + 5x3 + 4x4 = 0
2 x1 + 3 x2 + 6 x3 + 8 x4 = 0
x1 – 6 x2 – 9 x3 – 20 x4 = 0
4x1 + x2 + 4x3 + x4 = 0
5)
2x1 + 5x2 + x3 + 3x4 = 0
4 x1 + 6 x2 + 3 x3 + 5 x4 = 0
4x1 + 14x2 + x3 + 7x4 = 0
2x1 – 3x2 + 3x3 + x4 = 0
6)
2x1 – x2 + 3x3 + 4x4 = 0
4 x1 – 2 x2 + 5 x3 + 6 x4 = 0
6x1 – 3x2 + 7x3 + 8x4 = 0
x1 – 4x2 + 9x3 + 10x4 = 0
7)
2x1 + 3x2 + x3 + 2x4 = 0
4 x1 + 6 x2 + 3 x3 + 4 x4 = 0
6x1 + 9x2 + 5x3 + 6x4 = 0
8x1 + 12x2 + 7x3 + x4 = 0
8)
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
9)
(1 + )x1 + x2 + x3 = 0
x1 + (1 + ) x2 + x3 = 0
x1 + x2 + (1 + ) x3 = 0
10)
( + 1) x1 + x2 + x3 = 0
x1 + ( + 1) x2 + x3 = 0
x1 + x2 + ( + 1) x3 = 0
11)
x1 + 2 x2 + 3 x3 = 0
2x1 + 2x2 + 2x3 = 0
5x1 + 6x2 + 7x3 = 0
12)
2 x1 – x2 + x3 = 0
x1 – 2 x2 – 2 x3 = 0
x1 + x2 + 3 x3 = 0
13)
(–1 + 2 ) x1 + x2 + x3 = 0
x1 + x2 + x3 = 0
x1 + x2 + x3 = 0
14)
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
15)
x1 + 2x2 – x3 = 0
4x1 – x2 + 3x3 = 0
4x1 – x2 + x3 = 0
3x1 + x2 + 4x3 = 0
16)
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 + x4 = 0
17)
2x1 + x2 + 2x3 + 2x4 = 0
2 x1 + 9 x2 + 4 x4 = 0
2x1 + 5x2 + x3 + 3x4 = 0
2 x1 – 2 x2 + 3 x3 + x4 = 0
1) A = , B = ;
2) A = , B = ;
3) A = , B = ;
4) A = , B = ;
5) A = , B = ;
6) A = , B = ;
7) A = , B = ;
8) A = , B = ;
9) A = , B = ;
10) A = , B = ;
11) A = , B = ;
12) A = , B = ;
13) A = , B = ;
14) A = , B = ;
15) A = , B = .
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