Задачи по алгебре. Рудман Р.М. - 30 стр.

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Найти все значения λ, при которых вектор b линейно выражается
через векторы a
1
, a
2
, . . . , a
s
:
243.
a
1
= (2, 3, 5),
a
2
= (3, 7, 8),
a
3
= (1, −6, 1),
b = (7, −2, λ).
244.
a
1
= (4, 4, 3),
a
2
= (7, 2, 1),
a
3
= (4, 1, 6),
b = (5, 9, λ).
245.
a
1
= (3, 4, 2),
a
2
= (6, 8, 7),
b = (9, 12, λ).
246.
a
1
= (3, 2, 5),
a
2
= (2, 4, 7),
a
3
= (5, 6, λ),
b = (1, 3, 5).
247.
a
1
= (3, 2, 6),
a
2
= (7, 3, 9),
a
3
= (5, 1, 3),
b = (λ, 2, 5).
Найти все базы системы векторов:
248.
a
1
= (4, −1, 3, −2, )
a
2
= (8, −2, 6, −4),
a
3
= (3, −1, 4, −2),
a
4
= (6, −2, 8, −4).
249.
a
1
= (1, 2, 0, 0),
a
2
= (1, 2, 3, 4),
a
3
= (3, 6, 0, 0).
250.
a
1
= (1, 2, 3, 4),
a
2
= (2, 3, 4, 5),
a
3
= (3, 4, 5, 6),
a
4
= (4, 5, 6, 7).
251.
a
1
= (2, 1, −3, 1),
a
2
= (4, 2, −6, 2),
a
3
= (6, 3, −9, 3),
a
4
= (1, 1, 1, 1).
252.
a
1
= (1, 2, 3),
a
2
= (2, 3, 4),
a
3
= (3, 2, 3),
a
4
= (4, 3, 4),
a
5
= (1, 1, 1).
30

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