Методичка для тех.спец. математика
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x = 0 |
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z = cos 2 y . Этот случай уже рассматривался. Получили три |
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OC : |
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≤ π, |
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0 ≤ y |
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различных значения z : − |
1 |
,0,1. |
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8 |
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Ответ: − |
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− наименьшее значение, которое достигается во внутренней |
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π π |
8 |
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− наибольшее значение, которое достигается в граничных точ- |
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точке |
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; 1 |
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3 3 |
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ках (0,0), (π, π), (0, π), (π,0).
§4. КОНТРОЛЬНЫЕ РАБОТЫ КОНТРОЛЬНАЯ РАБОТА № 1
Элементы линейной алгебры. Аналитическая геометрия на плоскости и в пространстве
I. Исследовать и решить системы линейных алгебраических уравнений методом Гаусса:
3 x1 + x 2 − 4 x 3 + 2 x 4 + x 5 = 0, |
x1 + 2 x2 − 2 x3 − 3 x4 = 4, |
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1 − 2 x |
2 − 3 x 3 |
− 7 x 4 + 2 x 5 = 0, |
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+ 5 x2 − x3 − 4 x4 = 9, |
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1. 2 x |
2 x1 |
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+ 11x 2 + 34 x 4 − 5 x 5 = 0 |
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+ 3 x2 + x3 − x 4 = 5 |
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x1 |
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x1 |
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7 x1 + 2 x |
2 − x3 − 2 x 4 + 2 x5 = 0, |
x1 − 4 x 2 + 2 x3 + 3 x5 = 0, |
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− 3 x2 |
+ x3 − x4 − x5 = 0, |
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− 7 x 2 + 4 x3 + x 4 = 0, |
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2. x1 |
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2 x1 |
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+ x 4 + x5 = 0 |
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− 3 x2 + 2 x3 + x4 − 3 x5 = 0 |
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2 x1 + 3 x 2 + 2 x3 |
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x1 |
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x1 + x2 + 10 x3 + x 4 − x5 = 0, |
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x1 + 2 x2 − 3 x3 − 4 x 4 = 1, |
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+ 7 3 x 2 + x3 + 3 x 4 = 4, |
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3. 5 x1 − x2 + 8 x3 − 2 x4 + 2 x5 = 0, |
3 x1 |
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3 x |
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− 3 x |
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− 12 x |
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− 4 x |
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+ 4 x |
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= 0 |
2 x |
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+ 5 x |
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+ x |
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+ 3 x |
4 |
= 3 |
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6 x1 − 9 x |
2 + 21x |
3 − 3 x 4 − 12 x5 = 0, |
x1 − 5 x 2 + 3 x3 + 4 x 4 = 4, |
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− 4x1 + 6 x 2 − 14 x3 + 2 x4 + 8x5 = 0, |
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− 9 x 2 + 2x3 + x5 = 7, |
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4. |
2x1 |
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− x 4 − 4x5 = 0 |
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− 4 x2 − x3 − 4x4 + x5 = 3 |
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2 x1 − 3 x 2 + 7 x3 |
x1 |
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2 x1 − x 2 + 2 x3 − x 4 + x5 = 0, |
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x1 + 3 x2 − x3 − 2 x4 = 1, |
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+ 10 x 2 − 3 x3 |
− 2 x4 − x5 = 0, |
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+ 7 x 2 − 4 x3 − 3 x 4 = 3, |
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5. x1 |
2x1 |
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+ 4 x 2 − 3 x3 − x4 = 2 |
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4 x1 + 19 x 2 − 4 x3 − 5 x 4 − x5 = 0 |
x1 |
70
5 x1 − 2 x 2 + 9 x3 − 4 x4 − x5 = 0, |
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+ 4 x2 + 2 x3 + 2 x 4 − 5x5 = 0, |
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6. x1 |
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6 x |
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+ 2 x |
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+11x |
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− 2 x |
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− 6x |
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= 0 |
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12 x1 − 2 x |
2 + 7 x3 + 11x |
4 − x5 = 0, |
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2 + 14 x |
3 + 22 x 4 − 2x5 = 0, |
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7. 24 x1 − 2 x |
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+ x2 + x3 − x 4 |
+ 2x5 |
= 0 |
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x1 |
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x1 + 2 x2 + x3 + 4x 4 + x5 = 0, |
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8. 2 x1 + x 2 + 3 x3 + x 4 − 5x5 = 0, |
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+ 3x 2 − x3 + 6 x4 − x5 = 0 |
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x1 |
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2 x1 + 3 x2 + 3 x3 − 3 x 4 − x5 = 0, |
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+ 6 x2 − x3 + x 4 + 2x5 = 0, |
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9. x1 |
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+ 16 x 2 − 6 x3 + 6x 4 + 7x5 = 0 |
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x1 |
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x1 + 2 x 2 − x3 + x4 − x5 = 0, |
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10. x1 + x2 + 2x3 − x 4 + x5 = 0, |
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+ 3 x 2 + x3 = 0 |
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2 x1 |
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8 x1 + x 2 + x3 − x 4 + 2 x5 = 0, |
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− 3 x 2 − 2 x3 + x4 − 3x5 = 0, |
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11. 3x1 |
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5 x |
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+ 4 x |
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+ 3 x |
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− 2 x |
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+ 5x |
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= 0 |
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x1 + 3 x2 − x3 + 12 x 4 − x5 = 0, |
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− 2 x 2 + x3 − 10 x4 + x5 = 0, |
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12. 2x1 |
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3 x |
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+ x |
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+ 2 x |
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= 0 |
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7 x1 − 14 x 2 + 3 x |
3 − x 4 + x5 = 0, |
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− 2 x2 + x3 − 3 x 4 + 7x5 = 0, |
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13. x1 |
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5 x |
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− 10 x |
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+ x |
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+ 5 x |
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− 13x |
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= 0 |
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x1 + 2 x2 + 3 x3 + x 4 − x5 = 0, |
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− 2 x 2 − 6 x3 |
− 4 x 4 + x5 = 0, |
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14. 2x1 |
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3 x |
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− 2 x |
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+ 3 x |
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+ 3x |
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− x |
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= 0 |
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x1 + x2 + 4 x3 + 2 x5 = 0, |
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+ 4 x 2 + x3 + 3 x 4 = 1, |
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3 x1 |
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+ 3 x 2 − 3 x3 + 3 x 4 − 2x5 = 1 |
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2 x1 |
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x1 − 2 x 2 + 2 x3 + 3 x4 = 0, |
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− 3 x 2 + x3 + 4 x 4 = 1, |
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2x1 |
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3 x |
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− 5 x |
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+ 3 x |
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+ 7x |
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= 1 |
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x1 − x2 + 4x3 + 3 x 4 = 0, |
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− 2 x 2 + x3 + 2 x5 = 1, |
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3 x1 |
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− x 2 − 3 x3 − 3x4 + 2 x5 = 1 |
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2 x1 |
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x1 − 2 x 2 + 2 x3 + 3 x4 = 0, |
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− 5 x 2 + x3 + 4 x4 = 1, |
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3x1 |
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− 3 x 2 − x3 + x 4 = 1 |
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2 x1 |
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x1 − 3 x2 + 4 x3 + 3 x5 = 2, |
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− 8 x 2 + x3 + 2 x4 = 5, |
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3 x1 |
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− 5 x 2 − 3 x3 + 2 x4 − 3 x5 = 3 |
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2 x1 |
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x1 − 3 x2 + x3 + 2 x 4 = 4, |
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− 5 x 2 + 4 x3 + 3 x 4 = 7, |
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2x1 |
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− 2 x2 + 3 x3 + x 4 = 3 |
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x1 |
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x1 − x 2 + 3 x3 + 4 x4 = 0, |
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− 3 x 2 + x3 + 2x5 = 1, |
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4x1 |
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3 x |
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− 2 x |
2 |
− 2 x |
3 |
− 4 x |
4 |
+ 2x |
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= 1 |
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x1 + 4 x 2 − 2 x3 − 3 x4 = 2, |
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+ 9 x 2 − x3 − 4 x 4 = 5, |
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2x1 |
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+ 5 x2 + x3 − x 4 = 3 |
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x1 |
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x1 − 2 x 2 + 3 x3 + 4x5 = 1, |
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− 7 x 2 + 2x3 + x4 = 3, |
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4x1 |
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3 x |
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− 5 x |
2 |
− x |
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+ x |
4 |
− 4x |
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= 2 |
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71
x1 + x2 + x3 − x 4 − x5 = 0, |
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2x1 + x 2 |
− 2 x3 − x4 − 2x5 = 0, |
15. |
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+ 5 x3 − 2 x 4 − x5 = 0 |
x1 + 2 x2 |
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2 x1 + 2 x 2 − 2 x3 + x 4 − 3 x5 = 0, |
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+ 2x3 − x 4 + 2x5 = 0, |
16. 3x1 − x 2 |
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+ 4 x3 − 2 x4 + 5x5 = 0 |
x1 − 3 x2 |
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x1 + 2 x2 − 3 x3 + 10 x4 − x5 = 0, |
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− x1 − 2 x 2 + 3x3 + 10 x 4 + x5 = 0, |
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17. |
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− 9 x3 + 30 x4 − 3x5 = 0 |
x1 + 5 x 2 |
5 x1 + 6 x 2 − 2x3 + 7 x 4 + 4 x5 = 0,
2 x1 3x 2 − x3 + 4 x 4 + 2 x5 = 0,
5 x1 + 9 x2 − 3x3 + x 4 + 6 x5 = 0,+
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7 x1 |
+ 9x 2 |
− 3 x3 + 5 x 4 + 6 x5 |
= 0 |
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x1 − x 2 + 3 x3 + 4 x4 = 0, |
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− x 2 + 2 x3 + x 4 = 1, |
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2x1 |
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− 3 x 2 |
+ 8 x3 + 9 x 4 = 1 |
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4 x1 |
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x1 + x2 − 3x3 − 4 x4 = 1, |
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+ 5 x 2 |
− 2 x3 − x5 = 3, |
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4x1 |
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3 x |
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+ 4 x |
2 |
+ x |
3 |
+ 4x |
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− x |
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= 2 |
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x1 − 4 x 2 + 2 x3 + 3 x 4 = 5, |
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+ 4x3 + x 4 = 9, |
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2 x1 − 7 x 2 |
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x1 − 3 x2 + 2 x3 − 2 x4 = 4 |
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− x1 + 2 x |
2 − 3x3 + 2x 4 − 3 x5 = −3, |
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− 3 x 2 + x3 + 2 x 4 = 4, |
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− 2x1 + 5x 2 − 4 x3 − 3 x 4 = −7 |
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2 x1 − 2 x 2 − 3 x3 − 7 x 4 + 2 x5 = 0, |
x1 − 5 x2 + 3 x3 + 4 x 4 = 4, |
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+ 11x |
2 + 34 x3 − 5 x5 = 0, |
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− 9 x 2 |
+ 2 x3 + x 4 |
= 7, |
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19. x1 |
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2x1 |
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− 2 x3 − 16 x 4 + 3x5 = 0 |
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− 4 x 2 − x3 − 3 x 4 = 3 |
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x1 − 5 x2 |
x1 |
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3 x1 + x 2 − 8x3 + 2 x 4 + x5 = 0, |
x1 + 2 x2 − 3x3 − 4 x4 = 1, |
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+ 11x |
2 − 12 x3 − 5x5 = 0, |
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+ 7 x 2 |
− 2 x3 + x5 |
= 4, |
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20. x1 |
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3x1 |
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− 5 x2 |
+ 2 x3 + x4 + 3x5 = 0 |
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+ 5 x2 |
+ x3 + 4 x 4 |
+ x5 = 3 |
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x1 |
2 x1 |
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x1 + 3 x2 − 5 x3 + 9 x 4 − x5 = 0, |
x1 + x2 + 4 x3 + 2 x4 = 0, |
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+ 4 x 2 |
+ x3 + 3 x4 |
= 1, |
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21. 2x1 + 7 x 2 − 3 x3 − 7 x 4 + 2x5 = 0, |
3x1 |
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+ 4 x 2 + 2 x3 − 16 x 4 + 3x5 = 0 |
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+ 3 x 2 |
− 3 x3 + x4 |
= 1 |
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x1 |
2 x1 |
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5 x1 + 2 x2 − x3 + 3 x 4 + 4 x5 = 0, |
x1 + 3 x2 − x3 − 2 x5 = 1, |
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− 3 x3 + 3 x 4 + 5x5 = 0, |
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+ 7 x 2 |
− 4 x3 − 3x 4 = 3, |
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22. 3 x1 + x 2 |
2 x1 |
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6 x |
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+ 3 x |
2 |
− 2 x |
3 |
+ 4 x |
4 |
+ 5x |
5 |
= 0 |
x |
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+ 4 x |
2 |
− 3 x |
3 |
− 3 x |
4 |
+ 2x |
5 |
= 2 |
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3 x1 + 2 x2 − 2 x3 − x4 + 4 x5 = 0, |
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+ 5 x2 − 3 x3 − 2 x4 + x5 = 0, |
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23. 7 x1 |
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+ x2 + x3 − 7x5 = 0 |
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x1 |
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6 x1 + 3 x 2 − 2x3 + 4 x 4 + 7 x5 = 0, |
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7x1 |
+ 4 x 2 − 3 x3 + 2 x |
4 + 4x5 = 0, |
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24. |
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+ x2 − x3 − 2 x 4 − 3x5 = 0 |
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x1 |
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3 x1 − 5 x2 + 2 x3 + 5 x |
4 = 0, |
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7 x1 |
− 4 x 2 + x3 + 3 x4 |
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= 0, |
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25. |
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5 x |
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+ 7 x |
2 |
− 4 x |
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− 9 x |
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= 0 |
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x1 + x2 + 3 x3 − 2 x 4 + 3 x5 = 0, |
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2x1 |
+ 2 x 2 + 5x3 − x 4 + 3x5 = 0, |
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26. |
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+ x2 + 4 x3 − 5 x 4 + 6 x5 = 0 |
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x1 |
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x1 + 2 x2 + 3 x3 − 2 x 4 + x5 = 0, |
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+ 2 x2 + 7 x3 − 4 x 4 |
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+ x5 = 0, |
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27. x1 |
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+ 2 x2 +11x3 − 6 x 4 |
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+ x5 = 0 |
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x1 |
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6 x1 + 3 x 2 + 2 x3 + 3 x |
4 + 4 x5 = 0, |
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4 x1 |
+ 2 x 2 + x3 + 2 x4 |
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+ 3 x5 = 0, |
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28. |
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+ x 2 + x3 + x4 + x5 = 0 |
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2 x1 |
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3 x1 + 2 x 2 + 4 x3 + x4 + 2 x5 = 0, |
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+ 2 x 2 − 2 x3 + x4 |
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= 0, |
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29. 3 x1 |
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3 x |
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+ 2 x |
2 |
+16 x |
3 |
+ x |
4 |
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+ 6 x |
5 |
= 0 |
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x1 + x2 + x3 + 2 x4 + x5 = 0, |
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30. x1 − 2 x 2 − 3 x3 + x4 − x5 = 0, |
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− x 2 − 2 x3 + 3 x 4 |
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= 0 |
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2 x1 |
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x1 − x 2 + x3 − 2 x 4 + x5 = 0, |
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+ x 2 − 2 x3 − x 4 + 2 x5 = 0, |
31. x1 |
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− 3 x 2 + 4 x3 − 3 x4 = 0 |
x1 |
2 x1 + 3 x 2 + 5x3 = 0,
x1 + 3 x2 + 4 x3 = 0
x1 − x2 + 4 x3 + 3 x 4 = 0, |
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− 2 x 2 |
+ x3 + 2 x4 = 1, |
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3 x1 |
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− x 2 − 3 x3 − x4 = 1 |
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2 x1 |
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x1 − 2 x2 + 2 x3 + 3 x 4 = 0, |
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− 3 x 2 |
+ x3 + 4x5 = 1, |
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2 x1 |
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3 x |
1 |
− 5 x |
2 |
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+ 3 x |
3 |
+ 3 x |
4 |
+ 4x |
5 |
= 1 |
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x1 − 3 x2 + 4 x3 + 3 x 4 = 2, |
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− 8 x2 |
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+ x3 + 2 x 4 = 5, |
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3 x1 |
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− 5 x 2 |
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− 3 x3 − x4 = 3 |
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2 x1 |
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x1 − 2 x2 + 2 x3 + 3 x5 = 0, |
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− 5 x2 |
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+ x3 + 4 x 4 = 1, |
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3 x1 |
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− 3 x 2 |
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− x3 + 4 x 4 − 3 x5 = 1 |
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2 x1 |
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x1 − x2 + 3 x3 + 4 x 4 = 0, |
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− 3 x 2 |
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+ x3 + 2 x4 = 1, |
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4 x1 |
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3 x |
1 |
− 2 x |
2 |
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− 2 x |
3 |
− 2 x |
4 |
= 1 |
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x1 − 3 x2 + x3 + 2 x 4 = 4, |
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− 5 x2 |
+ 4 x3 + 3 x5 = 7, |
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2 x1 |
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− 2 x2 + 3 x3 − 2 x 4 + 3x5 = 3 |
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x1 |
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x1 − 2 x 2 + 3 x3 + 4 x4 = 1, |
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− 7 x 2 + 2 x3 + x 4 = 3, |
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4 x1 |
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3 x |
1 |
− 5 x |
2 |
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− x |
3 |
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− 3 x |
4 |
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= 2 |
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x1 + 4 x2 − 2 x3 − 3 x5 = 2, |
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+ 9 x 2 |
− x3 − 4 x 4 = 5, |
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2 x1 |
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+ 5 x 2 + x3 − 4 x 4 = 5 |
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x1 |
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x1 + x 2 − 3 x3 − 4 x 4 = 1, |
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+ 5 x2 |
− 2 x3 − x 4 = 3, |
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4 x1 |
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3 x |
1 |
+ 4x |
2 |
+ x |
3 |
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+ 3 x |
4 |
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= 2 |
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x1 + x 2 + x3 = 4, |
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− x 2 − x3 = 0 |
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x1 |
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x1 − x2 + 6 x3 = 0,
2 x1 + 3 x2 − x3 = 0
2 x1 + x 2 + x3 = 0,
7 x1 − 3 x 2 + 4 x3 = 0
x1 + x2 + x3 = 0,
x1 − x 2 − x3 = 0
4 x1 + x2 + 5 x3 + x 4 = 0,
− x1 + 6 x 2 + 4 x3 = 0
x1 + x2 + x3 = 0,
x1 − x 2 + 5 x3 + x 4 = 0
2 x1 + 3 x 2 + 5 x3 + 6 x |
4 = 0, |
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3 x1 + 4 x 2 + 6 x3 + 7 x 4 = 0, |
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38. |
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3 x1 + x 2 + x3 + 4 x 4 = 0 |
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8 x1 − 5 x 2 − 6 x3 + 3 x |
4 = 0, |
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4 x1 − x 2 − 3 x3 + 2 x4 |
= 0, |
39. |
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12 x1 − 7 x 2 − 9 x3 + 5 x 4 = 0 |
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x1 + 3 x2 + 7 x3 + x 4 = 0, |
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5 x 2 + 10 x3 + 5 x4 = 0, |
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40. |
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− 2 x1 + 7 x 2 + 12 x3 + 11x 4 = 0 |
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− x1 + 3 x 2 + 5 x 4 = 0, |
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= 0, |
41. 2 x1 + x 2 + 7 x3 − 3 x4 |
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= 0 |
4 x1 − x 2 + 11x3 − 9 x4 |
2 x1 + 3 x2 + 5 x 4 + 5 x5 = 0, |
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42. 6 x1 + 3 x 2 − x3 + 2 x 4 − 5 x5 = 0, |
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− 4 x1 − 2 x 2 |
− 2 x4 + 2 x5 = 0 |
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x1 − 2 x 2 − x |
3 − 3 x4 + 3 x5 = 0, |
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43. 2 x1 + 3 x2 + 5 x3 + x 4 − x5 = 0, |
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x 2 + x3 + x 4 |
− x5 = 0 |
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73
2 x1 + x 2 − x3 = 2, |
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− x1 + 3 x 2 + 4 x3 = 6 |
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3 x1 − x2 + x3 = 4, |
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x1 − 7 x 2 − x3 = 0 |
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x1 − x2 − 5 x3 = 0, |
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x1 + 2 x 2 + x3 = −3 |
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x1 + 4 x2 + 3x3 − 2 x4 = −6, |
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− 2 x1 + 7 x 2 + 9 x3 − 11x 4 = −18, |
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− 3 x1 + 5 x 2 + 8 x3 −11x 4 = −16 |
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x1 + 3 x2 + 5 x3 = −1, |
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6 x 2 + 12 x3 − 6 x 4 = −6, |
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− 2 x1 − 6x 2 − 10 x3 = 2 |
5 x1 + x 2 − 2 x3 − 4 x 4 = 5, |
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+ 7 x 4 = −20, |
10 x1 + 2 x 2 + 11x3 |
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+ 11x 4 = −13 |
− 15 x1 − 3 x 2 + 5 x3 |
3 x1 + x2 − 2 x3 = 9, |
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+ 2 x 2 + 4 x3 + 8 x4 = −16, |
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6 x1 |
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− 15 x1 − 5x 2 + 3 x3 − 7 x 4 = −17 |
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x1 + x 2 + x3 − x 4 = 1, |
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+ x 2 + 2 x3 − x4 = −1, |
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2 x1 |
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+ 2x 2 + 3 x3 − 2 x 4 = 0 |
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2 x1 |
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3 x1 + 2x 2 − 4 x3 + 2 x 4 = 2, |
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− 2 x 2 + 3 x3 − 3 x5 = −3, |
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x1 |
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+ 2 x3 − 3 x4 + 5 x5 = 4, |
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2 x1 |
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5 x |
1 |
− 3 x |
2 |
+ 4 x |
3 |
+ 2 x |
4 |
− 7 x |
5 |
= 2 |
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x1 + 2x 2 + 3 x3 − 2 x4 + x5 = 4, |
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+ 6 x 2 + 5 x3 − 4 x5 + 3 x5 = 5, |
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3 x1 |
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+ 2 x 2 + 7 x3 − 4 x 4 + x5 = 11, |
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x1 |
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+ 4 x 2 + 2 x3 − 3 x 4 + 3 x5 = 6 |
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2 x1 |
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x1 − 3 x2 + x3 + 2 x4 = 4, |
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− 5 x 2 + 4 x3 + 3 x5 = 7, |
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2 x1 |
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− 2 x 2 + 3 x3 − 2 x4 + 3 x5 = 3 |
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x1 |
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74 |
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x1 + x2 − 2 x3 + x 4 + x5 = 0, |
5 x1 + x2 + 3 x3 − 2 x 4 + 3x5 = 1, |
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2 x1 − x 2 + x3 + 2 x4 + x5 = 0, |
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15 x1 + 4 x 2 + 2 x3 − − 6 x 4 − x5 = 2 |
44. |
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3 x1 + x 2 − 6 x3 + 3 x4 + 3 x5 = 0 |
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− 18 x1 + 4 x2 + 2 x3 − 4 x4 = 1, |
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x1 − 2 x 2 + x3 + x 4 − 2 x5 = 0, |
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45. |
2 x1 + x 2 − 2 x3 + x4 − x5 = 0 |
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− 6 x1 − 2 x2 − 2 x3 + 3 x4 + 3 x5 = 2, |
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12 x1 − 2 x2 + 3 x3 − x 4 + x5 = 3 |
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− 2x1 + x 2 − 3 x3 + x4 = 0, |
7 x1 + 2 x 2 − 2 x3 + 2 x 4 − x5 = 3, |
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x1 − 2 x2 + x3 − 3x 4 = 0, |
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14 x1 + 3 x 2 + x3 − 3 x 4 − 2 x5 = 2 |
46. |
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5 x1 − x 2 + 4 x3 + 2x4 = 0 |
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9 x1 + 4 x 2 − 2 x3 + 5 x4 − x5 = 2, |
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2 x1 − x 2 + x3 − 2 x 4 − x5 = 0, |
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47. |
4 x1 + x 2 − x3 − 3 x 4 + x5 = 0 |
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− 3 x1 − 3 x 2 + 2 x3 − 3 x4 + 2 x5 = 3, |
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6 x1 + x 2 − 4 x3 + 2 x 4 − x5 = 1 |
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− 3 x1 + x 2 − x3 + 3x 4 + 2 x5 = 0, |
4 x1 + 2 x 2 + 2 x3 + 2 x4 − x5 = 4, |
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6 x1 − 2 x 2 + 3 x3 − x4 − x5 = 0, |
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12 x1 + 5 x 2 − x3 + 3 x4 + 3 x5 = 1 |
48. |
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x1 + x2 − 4 x3 + x 4 − 3x5 = 0 |
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21x1 + 3 x 2 + 2 x3 − 4 x 4 + 3 x5 = 3, |
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3 x1 + x 2 + x3 − 3x4 − x5 = 0, |
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49. |
6 x1 − 3 x 2 − x3 + x4 + 4 x5 = 0 |
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7 x1 + 2 x 2 − 3 x3 + x 4 − 2 x5 = 1, |
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14 x1 − 3 x 2 + 2 x3 − x 4 + x5 = 2 |
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3 x1 − 4 x 2 + x3 − 2 x4 = 0, |
6 x1 − x 2 − 2 x3 − 2 x4 − 4 x5 = 3, |
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9 x1 + 7 x 2 − x3 + 3x4 = 0, |
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12 x1 + x 2 + 2 x3 − 2 x4 − x5 = 1 |
50. |
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6 x1 − 3x 2 + 2 x3 − x 4 = 0 |
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15 x1 − 12 x 2 − x3 + 3 x 4 − x5 = 2, |
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4 x1 − x 2 − 2 x3 − x 4 − 5 x5 = 0, |
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51. |
8 x1 + x2 + 2 x3 + x 4 + 2 x5 = 0 |
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x1 + x2 − 10 x3 + x 4 + 5 x5 = 3, |
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− 3 x1 + 2 x 2 + 6 x3 − 2 x 4 + x5 = 4 |
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8 x1 + 2 x 2 + x3 − x4 + 2 x5 = 0, |
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3 x1 + x2 − 3 x3 − 2 x 4 + x5 = 2, |
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4 x1 + 2 x 2 − 3 x3 + x4 − 3 x5 = 0, |
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9 x1 − 2 x 2 + 2 x3 + x 4 − 4 x5 = 3 |
52. |
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12 x1 − 3x 2 + 2 x3 − 2 x 4 + x5 = 0 |
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75
5 x1 + x 2 + x3 + 2x4 − x5 = 0, |
− 8 x1 + x 2 − 3 x3 + x 4 + 2 x5 = 3, |
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53. |
10 x1 − 3 x 2 |
− x3 − x 4 |
+ 5 x5 |
= 0 |
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− 12 x1 − 2 x2 + x3 − 2x4 − 2 x5 = 4, |
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4 x1 + x 2 − 2 x3 + x 4 − x5 = 2 |
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15 x1 − 10 x2 − 3 x3 + x 4 = 0, |
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54. |
x1 + x2 − 10 x3 + 12x 4 = 0, |
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− 3 x1 + 2 x 2 + 6 x3 − x 4 = 0 |
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55. |
6 x1 − x 2 − 3 x3 − x 4 − 4 x5 = 0, |
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12 x1 + x 2 + 2 x3 + x4 − x5 = 0 |
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9 x1 + 4 x 2 − x3 + 5x4 − x5 = 0, |
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− 3 x1 − 3 x 2 + 2 x3 − 3x4 + 2 x5 = 0, |
56. |
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6 x1 + x 2 − 4 x3 + 2 x4 − x5 = 0 |
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57. |
7 x1 + 2 x 2 − x3 + 2x 4 + x5 = 0, |
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14 x1 − 3 x 2 + x3 − x 4 − 2x5 = 0 |
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− 10 x1 + 5 x 2 − x3 + 2x 4 = 0, |
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5 x1 − x 2 + 3 x3 − x 4 = 0, |
58. |
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− 15 x1 + 2 x 2 − 2 x3 + x 4 = 0 |
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59. |
8 x1 − 2 x 2 + x3 + 5x 4 − 3 x5 = 0, |
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16 x1 + 2 x 2 − 2 x3 + x4 − x5 = 0 |
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4 x1 + x 2 − 3 x3 + 4x 4 − 2 x5 = 0, |
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− 2 x1 − x2 + 2 x3 − 3x4 + x5 = 0, |
60. |
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6 x1 + 2x 2 − 4 x3 + x 4 − 3x5 = 0 |
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61. |
9 x1 − x 2 − 4 x3 − x 4 + 4 x5 = 0, |
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18 x1 + 3 x 2 + x3 + 3x 4 − 5 x5 = 0 |
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4 x1 + 2x 2 + x3 − 2 x 4 = 0, |
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14 x1 − 6 x2 − 3 x3 + x 4 = 0, |
62. |
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− x1 + x2 + 2 x3 − x 4 = 0 |
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5 x1 + x2 + x3 + 2 x 4 − x5 = 2, |
||||
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10 x1 |
− 3 x 2 |
− 2 x3 − x 4 + 4 x5 = 1 |
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8 x1 + 2 x2 + 3 x3 − x 4 + 2 x |
5 = 4, |
|||
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= 2, |
4 x1 + 2 x 2 − x3 + 2x 4 − 3 x5 |
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12 x1 |
− 3 x 2 |
+ 2 x3 − x 4 _ x5 |
= 3 |
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2 x1 − 2 x 2 + x3 − 3 x4 − 4 x5 = 1, |
||||
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6 x1 |
+ 3 x 2 |
− 2 x3 + 2x 4 − x5 |
= 4 |
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6 x1 − 3 x 2 − 2 x3 + x 4 − 3 x5 = 3, |
|||
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− 4 x1 + x 2 |
+ x3 − 3x 4 + 2 x5 |
= 4, |
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2 x1 − 2 x 2 |
+ x3 − 2 x 4 + 5 x5 |
= 5 |
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4 x1 − x 2 − 3 x3 − x 4 − 5 x5 = 4, |
||||
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8 x1 |
+ x 2 |
+ 2 x3 + 2x 4 + x5 |
= 3 |
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3 x1 − 4 x 2 + 2 x3 − x4 + 2 x5 = 4, |
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9 x1 + 7 x 2 − 2 x3 + 3x4 − x5 = 5, |
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6 x1 − 3 x 2 + x3 − 2 x 4 + 3 x5 = 5 |
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x1 + x2 + 2 x3 − 5 x 4 + x5 = 3, |
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3 x1 − 2 x 2 + 2 x3 − x 4 − 3 x5 = 4 |
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8 x1 − 3 x2 + 2 x3 − 3 x 4 + 2 x5 = 5, |
|
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− 4 x1 + x 2 − x3 + 2x 4 − x5 = 3, |
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12 x1 − 2 x 2 + 3 x3 − 2 x 4 + x5 = 4 |
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3 x1 + x 2 + 2 x3 − 3 x4 − x5 = 4, |
|
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6 x1 − 3 x 2 − x3 + 2x 4 4 x5 = 2 |
|
76
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10 x1 + x 2 − 2 x3 + 3x 4 − 2 x5 = 0, |
− 3 x1 + 4 x 2 − 2 x3 + 3 x 4 + x5 = 4, |
|
63. |
20 x1 + 3 x 2 + x3 + 2x 4 − 3 x5 = 0 |
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6 x1 − 2 x 2 + 3 x3 − 2x 4 − x5 = 5, |
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x1 + x2 − 4 x3 + 3 x4 − x5 = 6 |
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8 x1 − 3 x 2 + x3 − 3x4 + 2 x5 = 0, |
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10 x1 + x 2 − 2 x3 + 3x 4 − 2 x5 = 2, |
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− 4 x1 + x 2 − 2 x3 + x 4 − x5 = 0, |
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20 x1 + 3 x 2 + x3 + 3x 4 − 2 x5 = 4 |
64. |
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12 x1 − 2x2 + 3 x3 − x 4 + x5 = 0 |
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x1 + x2 + 4 x3 − 5x 4 + x5 = 0, |
7 x1 + 2 x 2 + 3 x3 − 2 x 4 + x5 = 5, |
|
65. |
3 x1 − 2 x 2 + 3 x3 − x 4 − 2 x5 = 0 |
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14 x1 − 6 x2 − 3 x3 + x 4 − 2 x5 = 6, |
||
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− x1 + x 2 + 2 x3 − x 4 + 5 x5 = 4 |
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6 x1 − 3 x 2 − x3 + 2 x4 = 0, |
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2 x1 − x 2 + 3 x3 − 2 x 4 − x5 = 1, |
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− 4 x1 + x 2 + 2 x3 − 3 x4 = 0, |
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4 x1 + x 2 − 2 x3 − 3x4 + x5 = 3 |
66. |
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2 x1 − 2x 2 + x3 − x4 = 0 |
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2 x1 − 2 x 2 + x3 − 4x 4 − 5 x5 = 0, |
− 3 x1 + 4 x 2 − x3 + 5 x 4 + x5 = 6, |
|
67. |
6 x1 + 3 x 2 − 2 x3 + x4 − 3 x5 = 0 |
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6 x1 − 2 x 2 + 3 x3 − 2x 4 − 2 x5 = 4, |
||
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4 x1 + x 2 − 2 x3 + 2x 4 + x5 = 0, |
x1 + x2 − 4 x3 + 3 x4 − x5 = 5 |
|
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9 x1 + x 2 − 3 x3 + x 4 + 4 x5 = 1, |
||
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− 8 x1 − 2 x 2 + 3 x3 − x 4 − 2 x5 = 0, |
|
18 x1 + 3 x 2 + x3 + 2x4 − 5 x5 = 5 |
68. |
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||
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12 x1 + 2x 2 − 3 x3 + x 4 + 2x5 = 0 |
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4 x1 + x 2 − x3 + 3 x 4 − 2 x5 = 5, |
||
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3 x1 + x 2 − 3 x3 − x 4 + 2 x5 = 0, |
||
69. |
9 x1 − 2 x 2 + x3 + 2x 4 − 4 x5 = 0 |
|
− 2 x1 − x 2 + 3 x3 − x 4 + 3 x5 = 6, |
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||
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|
6 x1 + 2 x 2 − x3 + 2 x 4 − 3 x5 = 7 |
|
− 21x1 + 4 x 2 + x3 − 4x 4 = 0, |
|
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|
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x1 − 2 x 2 − x3 + 2 x4 − 2 x5 = 2, |
|
|
7 x1 + 2 x 2 − 2 x3 + x 4 = 0, |
|
2 x1 + x 2 − 2 x3 + x4 − 3 x5 = 5 |
70. |
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||
|
14 x1 − 3x 2 + 3 x3 − x 4 = 0 |
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4 x1 − 2 x 2 + x3 + 2x 4 − x5 = 0, |
|
x1 + x2 − 2 x3 + 3 x 4 + 2 x5 = 6, |
71. |
12 x1 + 5 x 2 − x3 + x4 + 3 x5 = 0 |
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|
2 x1 − x 2 + x3 + 2x4 − x5 = 7, |
||
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3 x1 + x2 − 4 x3 + 3 x 4 + 3 x5 = 5 |
|
− 3 x1 + 3 x 2 + x3 − 4 x 4 − x5 = 0, |
|
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|
8 x1 − 2 x 2 + x3 − 4 x 4 − 3 x5 = 3, |
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x1 + 3 x2 + 2 x3 − x 4 − 3 x5 = 0, |
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16 x1 + 2 x 2 − 2 x3 + 3x 4 − x5 = 5 |
72. |
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2 x1 − 3x 2 + 3 x3 − x 4 + 2 x5 = 0 |
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5 x1 + x2 + 5 x3 − 2x 4 + 3 x5 = 0,
73.
15 x1 − 4 x 2 + x3 − 6 x 4 − x5 = 0
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x1 + 5 x 2 − 3 x3 − 2 x 4 = 0, |
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− 2 x1 + x3 + 4x 4 = 0, |
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74. |
− x1 − 3x 2 + 5 x3 + 2 x 4 = 0 |
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5 x |
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− x |
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+ 6 x |
3 |
− 2 x |
4 |
= 0 |
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2x1 + 6 x 2 − 2 x3 − 4 x4 = 0, |
− 5 x1 − 2x 2 − x3 4 = 0,
− 4x1 + 14x 2 − 8 x3 − 2 x 4 = 0+ 5x
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+ 10x 2 |
− 5 x3 − 3 x4 |
= 0 |
− x1 |
3 x1 + 2 x 2 + 2 x3 + x4 = 0,
3 x1 x 2 − x3 + 4x 4 = 0,
2x1 + 3 x 2 + 5 x3 − 2 x4 = 0− +
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− 4 x3 |
+ 7 x4 |
= 0 |
2 x1 |
x1 − 3 x2 − 3 x3 + x 4 = 0,
2 x1 2 x 2 + x3 + 3x4 = 0,
5x1 − 11x 2 − 8 x3 + 6 x 4 = 0−
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1 |
− x |
2 |
+ 5 x |
3 |
+ 5 x |
4 |
= 0 |
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x1 |
+ 3 x 2 − x3 +12x4 − x5 = 0, |
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78. 2 x1 − 2 x 2 + x3 − 10x 4 + x5 = 0, |
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3 x1 + x 2 + 2 x4 = 0 |
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2 x1 − x 2 + 3 x3 − x 4 − x5 = 0, |
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+ 5 x 2 − x3 + x 4 + 2 x5 = 0, |
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79. |
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x1 + 16x 2 − 6 x3 + 4 x 4 + 7 x5 = 0 |
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77
− 10 x1 + 5 x 2 − x3 + 2 x 4 + 2 x5 = 7, |
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5 x1 − x2 + 3 x3 − 5x 4 + x5 = 5, |
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− 15 x1 + 2 x2 − x3 + 2 x 4 − x5 = 6 |
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− 3 x1 + 4 x2 + x3 = 17, |
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2 x1 + x 2 − x3 = 0, |
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− 2 x1 + 3 x 2 + 5 x3 = 8 |
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x1 + 3 x2 − 2 x 4 = 3, |
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− x1 + 4 x3 − x 4 = 0, |
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x1 − x2 + 3 x3 + 3 x 4 = 6 |
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3 x |
1 |
+ 2 x |
2 |
− x |
3 |
+ 2 x |
4 |
= −3 |
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3 x1 + x 2 − x3 = 10, |
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− 3 x1 + 3 x 2 + 2 x3 = 8, |
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5 x1 + 2 x 2 + 8 x3 = −1 |
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− x1 + 2 x 2 − 2 x3 + 4 x 4 = 2, |
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− 8 x2 |
+ 4 x3 − 12 x4 = 4, |
5 x1 |
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4 x1 |
− 7 x 2 |
+ 5 x3 − 12 x4 = −1 |
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− 3 x 2 |
+ x3 − 4 x 4 = 3 |
2 x1 |
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6 x1 + x 2 − 4 x3 = −1, |
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+ 4 x 2 |
− 3 x3 = 3, |
4 x1 |
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3 x1 |
− 2 x 2 |
− 2 x3 = −3 |
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4 x1 + 2 x 2 − 3 x |
3 + 2 x 4 = 3, |
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+ x3 + 4 x 4 |
= 1, |
4 x 2 |
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3 x1 |
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+ 2 x 2 − 3 x3 + 4 x4 = 1 |
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+ 3 x 2 − 2x3 |
+ 2 x 4 = 2 |
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2 x1 |
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x1 + 2 x 2 + x3 + 4 x4 + x5 = 0, |
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80. 2 x1 − x 2 + 3x3 + x4 − 5x5 = 0, |
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x1 + 3x2 − x3 − 6 x4 − 5 x5 = 0 |
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− x1 − |
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x 2 = 0, |
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3 |
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3 x1 − 3 x2 = 0, |
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81. |
− |
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x1 + |
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x 2 = 0 |
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2 |
6 |
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12 x 2 = 0 |
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2 x1 − x 2 = 0, |
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2 x 2 = 0, |
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82. − 8 x1 + |
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4 x |
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− 2 x |
2 |
= 0 |
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x1 + x 2 − x3 = 0, |
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83. |
− x1 − x 2 + x3 = 0 |
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x1 + 2 x 2 + 3 x3 = 0, |
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84. 4 x1 + 5 x 2 + 6 x3 = 0, |
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7 x1 + 8 x 2 + 9 x3 = 0 |
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− x1 − x3 = 0,x 2 − x 4 = 0,
− x1 + x3 − x5 = 0,
− x 2 + x 4 − x6 = 0,
− x3 + x5 = 0,
− + =x 4 x6 0
x1 − 2 x 2 + 3 x3 = 0,
x1 2 x2 − 3 x3 = 0,
2 x1 − 4 x 2 + 6 x3 = 0,− +
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+ 6 x2 |
− 9 x3 |
= 0 |
− 3x1 |
78
x1 + x2 − 24 x 4 = −1, |
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− 2 x1 + x 2 + x3 + 2 x 4 = −1, |
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3 x1 − 2 x 2 − x3 − 2 x4 = 3 |
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7 x |
1 |
+ 5 x |
2 |
+ 2x |
3 |
+ 4 x |
4 |
= −8 |
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4 x1 − x 2 − 3 x3 + 2 x 4 = −1, |
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8 x1 − 5 x2 − 6x3 + 3x 4 = 2, |
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12x1 − 7x2 − 9 x3 + 5 x 4 = 3 |
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− 7 x1 − 5 x 2 − 2 x3 − x4 = 8, |
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− 3 x1 + 2 x 2 + x3 + 2x4 = −3, |
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2x1 − x 2 − x3 − 2 x4 = 1 |
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− x1 − x2 + 24 x4 = 1 |
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x1 − 2 x 2 − x3 + 3x4 = 5, |
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4 x1 + x 2 + x3 + 2x4 = 13, |
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7x1 + 4 x 2 + 3 x3 + x 4 = 21 |
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+ 5 x 2 + 3 x3 − 4 x4 = 3 |
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2x1 |
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2 x1 − 3 x 2 + 5 x3 + 6x 4 = 4, |
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6 x1 − 2 x 2 + 3x3 + 4x4 = 5, |
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3x1 − x2 + 3 x3 + x 4 = −8 |
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3x |
1 |
− x |
2 |
+ 2 x |
3 |
+ 2 x |
4 |
= −1 |
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3 x1 + 2 x 2 − x3 + 2x4 = −3, |
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− x1 − 3 x 2 + 2x4 = −3, |
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x1 − 4 x3 + 3 x3 + 3 x 4 = 0 |
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− x2 |
+ 3 x3 + 3 x 4 |
= 6 |
x1 |
3 x1 + 2 x2 − 3 x3 + 4x 4 = 1, |
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+ 3 x2 |
− 2x3 + 2x4 |
= 2, |
2 x1 |
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4x1 |
+ 2x 2 |
− 3 x3 + 2 x 4 |
= 3, |
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+ x3 |
+ 4 x 4 |
= 1 |
4x1 |