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Консультация № 177608
02.04.2010, 22:31
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Здравствуйте товарищи эксперты решите пожалуйста задачу.
Решите систему методом Крамера и сделайте проверку,
-2x+y+z=3
x-4y+2z=-13
2x+y+4z=10
Заранее спасибо!!!)))
Решите систему методом Крамера и сделайте проверку,
-2x+y+z=3
x-4y+2z=-13
2x+y+4z=10
Заранее спасибо!!!)))
Обсуждение
Неизвестный
02.04.2010, 23:16
общий
это ответ
Здравствуйте, Лялюшкин Александр Николаевич.
|-2 1 1|
|1 -4 2| - матрица A
|2 1 4 |
|3 1 1|
|-13 -4 2| - матрица D1
|10 1 4 |
|-2 3 1|
|1 -13 2| - матрица D2
|2 10 4 |
|-2 1 3|
|1 -4 -13| - матрица D3
|2 1 10 |
По формуле Крамера :
x= det(D1)/det(A)
y= det(D2)/det(A)
z= det(D3)/det(A)
det(A)= 45
det(D1)= 45
det(D2)= 180
det(D3)= 45
x=1, y=4, z=1
Проверим
|-2*1+1*4+1*1=3
|1*1-4*4+2*1=-13
|2*1+1*4+4*1=10
Ответ: x=1, y=4, z=1 или (1,4,1)
|-2 1 1|
|1 -4 2| - матрица A
|2 1 4 |
|3 1 1|
|-13 -4 2| - матрица D1
|10 1 4 |
|-2 3 1|
|1 -13 2| - матрица D2
|2 10 4 |
|-2 1 3|
|1 -4 -13| - матрица D3
|2 1 10 |
По формуле Крамера :
x= det(D1)/det(A)
y= det(D2)/det(A)
z= det(D3)/det(A)
det(A)= 45
det(D1)= 45
det(D2)= 180
det(D3)= 45
x=1, y=4, z=1
Проверим
|-2*1+1*4+1*1=3
|1*1-4*4+2*1=-13
|2*1+1*4+4*1=10
Ответ: x=1, y=4, z=1 или (1,4,1)
Форма ответа
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