1. Решите системы по формулам Крамера, матричным способом, методом
Гаусса:
а) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image202.gif)
|
б) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image204.gif)
|
в) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image206.gif)
|
г) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image208.gif)
|
д) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image210.gif)
|
е) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image212.gif)
|
ж) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image214.gif)
|
з) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image216.gif)
|
и) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image218.gif)
|
2. Исследуйте системы и в случае совместности решите их методом
Гаусса или Жордана-Гаусса:
а) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image220.gif)
|
б) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image222.gif)
|
в) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image224.gif)
|
г) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image226.gif)
|
д) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image228.gif)
|
е) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image230.gif)
|
ж) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image232.gif)
|
з) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image234.gif)
|
и) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image236.gif)
|
к) ![](%D0%A1%D0%B1%D0%BE%D1%80%D0%BD%D0%B8%D0%BA%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20%D0%BF%D0%BE%20%D0%B2%D1%8B%D1%81%D1%88%D0%B5%D0%B9%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5%20%20%C2%A71.3.%20%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D1%8B%20%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85%20%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9%20%C2%BB_files/image238.gif)
|
3. Решите однородные системы уравнений:
Ответы. 1. а) (2;3), б) (-1;2), в) (1;-1), г) (2;-1;1), д)
(4;5;-3), е) (0;3;‑3), ж) (2;1;0), з) (1;0;-1), и) (-1;0;2). 2. а)
(с; ; с), б) (с ; с ; ; ), в) (1; -1), г) Ø, д) (1; 0; 2), е) (5с-5;7с-7;с;0),
ж) Ø, з) Ø, и) (0; 1; 2), к) ( ). 3. а) (с; 2с; с), б) (0; 0; 0), в)( ), г)( ), д) ( ).
|