Задачи по алгебре. Рудман Р.М. - 37 стр.

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284.
2x
1
x
2
+ 3x
3
+ 4x
4
= 5,
4x
1
2x
2
+ 5x
3
+ 6x
4
= 7,
6x
1
3x
2
+ 7x
3
+ 8x
4
= 9,
λx
1
4x
2
+ 9x
3
+ 10x
4
= 11.
285.
2x
1
+ 3x
2
+ x
3
+ 2x
4
= 3,
4x
1
+ 6x
2
+ 3x
3
+ 4x
4
= 5,
6x
1
+ 9x
2
+ 5x
3
+ 6x
4
= 7,
8x
1
+ 12x
2
+ 7x
3
+ λx
4
= 9.
286.
λx
1
+ x
2
+ x
3
= 1,
x
1
+ λx
2
+ x
3
= 1,
x
1
+ x
2
+ λx
3
= 1.
287.
λx
1
+ x
2
+ x
3
+ x
4
= 1,
x
1
+ λx
2
+ x
3
+ x
4
= 1,
x
1
+ x
2
+ λx
3
+ x
4
= 1,
x
1
+ x
2
+ x
3
+ λx
4
= 1.
288.
(1 + λ)x
1
+ x
2
+ x
3
= 1,
x
1
+ (1 + λ)x
2
+ x
3
= λ,
x
1
+ x
2
+ (1 + λ)x
3
= λ
2
.
289.
(λ + 1)x
1
+ x
2
+ x
3
= λ
2
+ 3λ,
x
1
+ (λ + 1)x
2
+ x
3
= λ
3
+ 3λ
2
,
x
1
+ x
2
+ (λ + 1)x
3
= λ
4
+ 3λ
3
.
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