1.13 | a1 | a1x + b1y + c1 | b1 | = | a1 | b1 | c1 |
a2 | a2x + b2y + c2 | b2 | a2 | b2 | c2 | ||
a3 | a3x + b3y + c3 | b3 | a3 | b3 | c3 |
1.14 | a1 + b1x | a1 - b1x | c1 | = - 2x | a1 | b1 | c1 |
a2 + b2x | a2 - b2x | c2 | a2 | b2 | c2 | ||
a3 + b3x | a3 - b3x | c3 | a3 | b3 | c3 |
1.15 | 1 | a | a3 | = (a + b+ c) | 1 | a | a2 |
1 | b | b3 | 1 | b | b2 | ||
1 | с | с3 | 1 | с | с2 |
Решить уравнения:
1.16 | x | x + 1 | x + 2 | = 0 | 1.17 | cos 8x | – sin 5x | = 0 |
x + 3 | x + 4 | x + 5 | sin 8x | cos 5x | ||||
x + 6 | x + 7 | x + 8 |
1.18 | 3 | х | – х | = 0 |
2 | – 1 | 3 | ||
x + 10 | 1 | 1 |
Решить неравенства:
1.19 | 3 | – 2 | 1 | < 0 | 1.20 | 2 | x + 2 | – 1 | > 0 |
1 | х | – 2 | 1 | 1 | – 2 | ||||
– 1 | 2 | – 1 | 5 | – 3 | x |
Вычислить определители, понижая порядок:
1.21 | 1 | 1 | 1 | 1.22 | 1 | a | a2 | a3 |
x | y | z | 1 | b | b2 | b3 | ||
x2 | y2 | z2 | 1 | c | c2 | c3 | ||
1 | x | x2 | x3 |
1.23 | a | 1 | 1 | 1 | 1.24 | 2 | – 1 | 1 | 0 |
b | 0 | 1 | 1 | 0 | 1 | 2 | – 1 | ||
c | 1 | 0 | 1 | 3 | – 1 | 2 | 3 | ||
d | 1 | 1 | 0 | 3 | 1 | 6 | 1 |
1.25 |
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1.26 | 2 | 1 | 1 | 1 | 1 | 1.27 | 5 | 6 | 0 | 0 | 0 |
1 | 3 | 1 | 1 | 1 | 1 | 5 | 6 | 0 | 0 | ||
1 | 1 | 4 | 1 | 1 | 0 | 1 | 5 | 6 | 0 | ||
1 | 1 | 1 | 5 | 1 | 0 | 0 | 1 | 5 | 6 | ||
1 | 1 | 1 | 1 | 6 | 0 | 0 | 0 | 1 | 5 |
1.28 | x | 0 | – 1 | 1 | 0 | 1.27 | 1 + a | 1 | 1 | 1 |
1 | x | – 1 | 1 | 0 | 1 | 1 – a | 1 | 1 | ||
1 | 0 | x – 1 | 0 | 1 | 1 | 1 | 1 + b | 1 | ||
0 | 1 | – 1 | x | 1 | 1 | 1 | 1 | 1 – b | ||
0 | 1 | – 1 | 0 | x |
Вычислить определитель, используя теорему Лапласа
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