ഊഊഊഊ ഊ ഊ ഊ Векторные пространства - задание №17ഊ ഊഊ ഊ
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ഊ Векторные пространства
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ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ ഊ
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ഊ Докажите, что каждая из двух данных систем векторов является базисом соответствующего векторного пространства. Найдите связь между координатами одного и того же вектора в этих базисах, если:
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17.01.
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= (2; 3; 3), = (3; 1; 4),
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= (1; 2; 1), = (5; 2; 1),
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= (3; 7; 1), = (1; 1; –6);
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17.02.
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= (1; 2; 1; 1), = (–2; –3; –4; –4),
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= (1; 1; 1; 1), = (2; 2; 5; 4),
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= (1; 3; 2; 3), = (–2; –3; –5; –4),
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= (1; 1; 2; 1); = (1; 0; 3; 3);
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17.03.
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= (1; 0; 2; 1), = (1; 3; 0; 2),
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= (1; 1; 1; 1), = (0; 1; 1; –3),
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= (2; 0; 1; 3), = (2; 4; 3; 5),
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= (–2; 1; –2; 2); = (1; 0; –2; 4);
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17.04.
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= (1; 2; 1; 2), = (1; 0; 1; 2),
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= (1; 1; 1; 1), = (1; 2; 3; 4),
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= (1; 0; 1; 1), = (–1; –2; –3; 1),
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= (1; 1; 0; 2); = (0; 1; –1; 0);
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17.05.
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= (1; 1; 1; 1), = (1; 1; 1; 1),
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= (–1; 1; 1; –2), = (1;–1; 1; 2),
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= (1; 1; 2; 2), = (2; – 2; –1; 0),
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= (0; 1; –2; 1), = (1; 0; 1; 1);
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17.06.
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= (1; 0; –1), = (2; 12; –6),
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= (0; 2; 0), = (0; 8; –4),
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= (–1; 1; 0); = ( –2; –10; 4);
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17.07.
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= (–1; 0; –2), = (15; –8; 14),
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= (–1; –2; –1), = (–9; 2; –9),
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= (–1; 1; 0), = (–13; 7; –12);
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17.08.
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= (1; 0; –1), = (–4; 0; 7),
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= (–2; –2; 0), = (5; 2; –6) ,
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= (0; 0; 1), = ( –6; 0; 11);
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17.09.
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= (1; 2; 0; 1), = (1; 1; 2; 2),
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=(–1; –3; 1; –1), =(–1; –2; –2; 0),
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= (1; 1; –1; 1), = (1; 1; 3; –1),
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= (1; 1; –1; 1), = (2; 1; 2; 1);
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17.10.
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= (1; 2; 0; 1), = (1; 1; 2; 2),
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=(–1; –3; 1; –1), =(–1; –2; –2; 0),
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= (1; 1; –1; 1), = (1; 1; 3; –1),
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= (1; 1; –1; 1), = (2; 1; 2; 1);
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17.11.
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= (0; 1; 0;–1), = (1;–1; 2; –2),
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= (1; 1; 1; 0), = (2;–1; 3; –3),
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= (2; 0; 2; 1), = (–1; 0; –1; 4),
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= (1; 1; 1; 1), = (–2; 1; –5; 3);
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17.12.
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= (1; 2; 1; 2), = (0; 1; 3; 3),
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= (1; 1; 0;1), = (2; 1; 1; –1) ,
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= (1; –1; 2; 0), = (1; –1; 2;–3),
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= (3; 2; –1; 1), = (3; –3; 0; 1);
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17.13.
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= (1; 2; 1), = (9; –2; 9),
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= (1; 0; 2), = (13; –7; 12),
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= (1; –1; 0), = (–15; 8; –14);
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17.14.
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= (–5; –2; 6), = (2; 2; 0),
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= (6; 0; –11), = (0; 0; –1) ,
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= (4; 0; –7), = ( –1; 0; 1);
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17.15.
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= (–1; –1; 6), = (–1; –2; –1),
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= (–3; –1; –4), = (–3; –7; –1),
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= (–5; –2; –1), = (–2; –3; –3);
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17.16.
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= (1; 1; 2; 1), = (1; 1; 4; 0),
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= (2; 1; 0; 1), = (2; 1; 1; 1) ,
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= (1; 2; 1; 2), = (3; 0; 1; 2);
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= (–1; 3; 2; 1), = (–1; 1; 1; 3);
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17.17.
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= (1; 2; 0; 1), = (1; 0; 2; 3),
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= (1; 1; 2; 3), = (2; 1; 3; 1),
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= (1; 2; 3; 0), = (–2; 3;–1; 0),
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= (1; 1; 1; 3), = (–1; 1; 3; 2);
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17.18.
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= (1; 2; 1; 1), = (1; 2; 0; 1),
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= (2; 2; 0; 2), = (2; 1; 3; 1) ,
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= (0; 4; 1; 1), = (1; 2; 3; 0),
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= (1; 1; 1; 3), = (–1; 1; 3; 2);
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17.19.
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= (1; 1; –1; –1), = (2; 2; 1; 1),
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= (2; 1; –4; 1), = (1; 1; 1; 1),
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= (1; 2; 2; 1), = (3; 2; 2; 1),
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= (2; 2; –1; 2), = (1; –2; –4; – 1);
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17.20.
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= (1; 0; –2; –3), = (1;–4;–1; 9),
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= (0; 1; 1; 0), = (–2; 6; 3; 0) ,
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= (3; 1; –3; –6), = (0; –7; –4; 0),
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= (2; 3; 8; 7), = (–3; 8; 0; –3);
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17.21.
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= (1; –4; –3), = (4; –1; 2),
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= (–2; 6; 3), = (0; 9; 1),
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= (3; 0; –3), = (1; 2; –5);
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17.22.
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= (2; –4; 1), = (1; –2; 3),
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= (3; –3; 2), = (–2; 2; –5) ,
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= (1; 0; –3), = (2; –3; 0);
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17.23.
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= (0; 4; –3), = (1; 5; –1),
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= (1; 2; 3), = (1; –1; –5),
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= (–2; 2; –1), = (2; 0; –1);
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17.24.
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ഊ 		ഊ
= (1; 2; 1; 1), = (1; 1; 1; 1),
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= (0; 1; 2; 1), = (0; 1; 2; 2) ,
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= (1; 1; 2; 1), = (1; 2; –1; –1),
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= (1; 0; 1; 2), = (–1; 2; –3; –1);
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17.25.
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ഊ 		ഊ
= (1; 1; –1; –1), = (0; 1; 2; 1),
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= (2; 1; –4; 1), = (1; 1; 0; 1),
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= (1; 2; 2; 1), = (0; –1; –2; 1),
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= (2; 2; –1; 2), = (–1; 0; 1; 1);
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17.26.
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ഊ 		ഊ
= (1; 0; –1; –1), = (1; 1;–1; 2),
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= (–1; 1; 2; –1), = (2; 3; 4; 1) ,
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= (2; –1; –1; 2), = (–2; –2; 3; –1),
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= (1; 1; 2; 3), = (1; 1; 2; –2);
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17.27.
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= (1; –2; 0; 7), = (1; 4; 0; 3),
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= (2; –3; –5; –4), = (–5; 1;–2; 5),
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= (–3; 0; 7; 0), = (–3; 1; –3; 0),
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= (3; 7; 9; 0), = (2; –7; 1; –4);
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17.28.
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ഊ 		ഊ
= (–1; 5; 2; 0), = (–7; 0; 1; –1),
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= (–3; 3; –7; 8), = (–5; –6; –8; –5),
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= (5; –2; 0; 4), = (–3; –2; 0; 2),
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= (2; –4; 0;–1), = (1; 9; 0; –3);
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17.29.
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ഊ 		ഊ
= (3; 1; 1; 2), = (1; 1; 2; –1),
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= (1; –2; –1; 3), = (2; –1;1; 0),
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= (2; –2; 4; –2), = (3; 1; 4; –1),
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= (–2; 2; –2; 4), = (–1; 3; 0; 2);
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17.30.
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ഊ 		ഊ
= (1; 1; 3; 2), = (–1; 1; 1; 1),
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= (3; –2; 1; –1), = (1; –1; –1; 1) ,
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= (–2; 4; –2; 1), = (–1; 2; –1; 1),
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= (1; –1; –2; 3), = (1; 2; 1; 1);
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17.31.
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ഊ 		ഊ
= (1; 1; 2; 2), = (1; 2; 3; 4),
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= (1; –2; –1; 3), = (3; 2; 1; 2) ,
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= (–2; 2; –2; 1), = (2; 1; 2; 3),
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= (3; –2; 1; –2), = (4; 3; 1; 1);
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17.32.
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ഊ 		ഊ
= (–1; 1; 1), = (5;–3; –5),
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= (–1; 0; 1), = (–7; 4; 7),
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= (0; 1;–2), = (6; –3; –8);
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17.33.
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ഊ 		ഊ
= (–2; –2; 1), = (–2; –2; 1),
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= (0; –2; 1), = (2; 8; –3) ,
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= (1; –1; 0), = (1; –1; 0);
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17.34.
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ഊ 		ഊ
= (1; 0; 1), = (–1; –4; –11),
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= (–1; 0; –1), = (1; 0; 1),
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= (0; –2; –2), = (–1; 0; –3);
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17.35.
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ഊ 		ഊ
= (–1; 0; –2), = (15; –8; 14),
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= (–1; –4; –1), = (–9; 2; –9),
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= (–1; 1; 0); = ( –13; 7; –12);
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17.36.
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ഊ 		ഊ
= (–2; –1; –2), = (6; 3; 6),
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= (0; –2; 0), = (0; –4; 0),
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= (–2; –2; –1); = (6; 16; 3).
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ഊ ഊഊ㰡ⴭ⁧潯杬攠慮慬楳琠ⴭ㸍਼獣物灴㸍ਠ
晵湣瑩潮⡩ⱳⱯⱧⱲⱡⱭ⥻楛❇潯杬敁湡汹瑩捳佢橥捴❝㵲㭩孲崽楛牝籼晵湣瑩潮⠩笍ਠ
楛牝⹱㵩孲崮煼籛崩⹰畳栨慲杵浥湴猩紬楛牝⹬㴱⩮敷⁄慴攨⤻愽献捲敡瑥䕬敭敮琨漩Ⰽਠ㵳⹧整䕬敭敮瑳䉹呡李慭攨漩嬰崻愮慳祮挽ㄻ愮獲挽朻洮灡牥湴乯摥⹩湳敲瑂敦潲攨愬洩ഊ†紩⡷楮摯眬摯捵浥湴Ⱗ獣物灴✬❨瑴灳㨯⽷睷⹧潯杬攭慮慬祴楣献捯洯慮慬祴楣献橳✬❧愧⤻ഊഊ†条⠧捲敡瑥✬‧啁ⴱ㠳㐰㈰㜭ㄧⰠ❡畴漧⤻ഊ†条⠧獥湤✬‧灡来癩敷✩㬍਍਼⽳捲楰琾ഊ㰡ⴭ⁧潯杬攠慮慬楳琠ⴭ㸍਍਼ℭⵒ慴楮杀䵡楬⹲甠捯畮瑥爭ⴾഊ㱳捲楰琠污湧畡来㴢橡癡獣物灴∾㰡ⴭഊ搽摯捵浥湴㭶慲⁡㴧✻愫㴧㭲㴧⭥獣慰攨搮牥晥牲敲⤻橳㴱〻⼯ⴭ㸼⽳捲楰琾ഊ㱳捲楰琠污湧畡来㴢橡癡獣物灴ㄮㄢ㸼ℭⴍ੡⬽✻樽✫湡癩条瑯爮橡癡䕮慢汥搨⤻橳㴱ㄻ⼯ⴭ㸼⽳捲楰琾ഊ㱳捲楰琠污湧畡来㴢橡癡獣物灴ㄮ㈢㸼ℭⴍੳ㵳捲敥渻愫㴧㭳㴧⭳⹷楤瑨⬧⨧⭳⹨敩杨琻ഊ愫㴧㭤㴧⬨献捯汯牄数瑨㽳⹣潬潲䑥灴栺献灩硥汄数瑨⤻橳㴱㈻⼯ⴭ㸼⽳捲楰琾ഊ㱳捲楰琠污湧畡来㴢橡癡獣物灴ㄮ㌢㸼ℭⴍ੪猽ㄳ㬯⼭ⴾ㰯獣物灴㸼獣物灴慮杵慧攽≪慶慳捲楰琢⁴祰攽≴數琯橡癡獣物灴∾㰡ⴭഊ搮睲楴攨✼愠桲敦㴢桴瑰㨯⽴潰⹭慩氮牵⽪畭瀿晲潭㴱㤰㜸㌳∠瑡牧整㴢彴潰∾✫ഊ✼業朠獲挽≨瑴瀺⼯摣⹣ㄮ扤⹡ㄮ瑯瀮浡楬⹲甯捯畮瑥爿楤㴱㤰㜸㌳㭴㴹㤻橳㴧⭪猫ഊ愫✻牡湤㴧⭍慴栮牡湤潭⠩⬧∠慬琽∿㼿㼿㼿䁍慩氮牵∠扯牤敲㴢〢‧⬍ਧ桥楧桴㴢ㄸ∠睩摴栽∸㠢㸼尯愾✩㭩昨ㄱ㱪猩搮睲楴攨✼✫✡ⴭ‧⤻⼯ⴭ㸼⽳捲楰琾ഊ㱮潳捲楰琾㱡⁴慲来琽≟瑯瀢⁨牥昽≨瑴瀺⼯瑯瀮浡楬⹲甯橵浰㽦牯洽ㄹ〷㠳㌢㸍਼業朠獲挽≨瑴瀺⼯摣⹣ㄮ扤⹡ㄮ瑯瀮浡楬⹲甯捯畮瑥爿橳㵮愻楤㴱㤰㜸㌳㭴㴹㤢‍੨敩杨琽∱㠢⁷楤瑨㴢㠸∠扯牤敲㴢〢⁡汴㴢㼿㼿㼿㽀䵡楬⹲產㸼⽡㸼⽮潳捲楰琾ഊ㱳捲楰琠污湧畡来㴢橡癡獣物灴∠瑹灥㴢瑥硴⽪慶慳捲楰琢㸼ℭⴍ੩昨ㄱ㱪猩搮睲楴攨✭ⴧ⬧㸧⤻⼯ⴭ㸼⽳捲楰琾ഊ㰡ⴭ⼯⁒慴楮杀䵡楬⹲甠捯畮瑥爭ⴾഊ†††††††††㱄䥖⁩搽摩癍敮甠执捯汯爽⍦ㅦㅦㄠ獴祬攽≖䥓䥂䥌䥔夺⁶楳楢汥㬠坉䑔䠺‱ば砻⁐体䥔䥏为⁡扳潬畴攻⁔佐㨠㄰灸㬠䡅䥇䡔㨠㄰灸∾ഊ†††††††††㱴慢汥⁢杣潬潲㴣昱昱昱⁣敬汓灡捩湧㴱⁣敬汐慤摩湧㴱⁷楤瑨㴢㄰〥∠䡥楧桴㴢㄰〥∠扯牤敲㴰⁳瑹汥㴢扯牤敲㨱灸‣捣捣捣⁳潬楤㬢㸼瑲㸼瑤⁳瑹汥㴢睩摴栺㌰ば砻‍੨敩杨琺㈵ば砻⁢潲摥爺ㅰ砠⍣捣捣挠獯汩搻∾ഊ㱳捲楰琠瑹灥㴢瑥硴⽪慶慳捲楰琢㸼ℭⴍ੧潯杬敟慤彣汩敮琠㴠≰畢ⴷ㠷㈱㌱㈹ㄴ㐴ㄹ㤢㬍ਯ⨠㌰へ㈵〬‿㼿㼿㼿‱㌮〹⸱〠⨯ഊ杯潧汥彡摟獬潴‽•㔰㐷ㄱ㌲〲∻ഊ杯潧汥彡摟睩摴栠㴠㌰〻ഊ杯潧汥彡摟桥楧桴‽′㔰㬍ਯ⼭ⴾഊ㰯獣物灴㸍਼獣物灴⁴祰攽≴數琯橡癡獣物灴∍ਾ㰯獣物灴㸍਼ℭⴠ奡湤數⹒呂⁒ⵁⴱㄹㄱ㌶〭㈠ⴭ㸍਼摩瘠楤㴢祡湤數彲瑢归ⵁⴱㄹㄱ㌶〭㈢㸼⽤楶㸍਼獣物灴㸍੷楮摯眮祡䍯湴數瑃戮灵獨⠨⤠㴾⁻ഊ††奡⹃潮瑥硴⹁摶䵡湡来爮牥湤敲⡻ഊ††††≢汯捫䥤∺•刭䄭ㄱ㤱ㄳ㘰ⴲ∬ഊ††††≲敮摥牔漢㨠≹慮摥硟牴扟刭䄭ㄱ㤱ㄳ㘰ⴲ∍ਠ†⁽⤍੽⤍਼⽳捲楰琾㰯瑤㸼⽴爾ഊ㱔刾㱔䐠慬楧渽捥湴敲⁨敩杨琽㈰灸⁢杣潬潲㴣挴挴挴㸼愠捬慳猽牥搠桲敦㴢⌢湣汩捫㴢扣汯獥⠩㬠牥瑵牮⁦慬獥㬢‾㱢㻇㰯戾㰯愾㰯呄㸼⽔刾ഊ㰯瑡扬放ഊ㰯䑉嘾ഊ†††††††㱓䍒䥐吾ഊ††ഊ०畮捴楯渠扣汯獥⠩ഊॻഊउ摩癍敮甮獴祬攮摩獰污礠㴠❮潮攧㬍ਉ納ਠ†‍਍੶慲⁩獄位‽
摯捵浥湴⹧整䕬敭敮瑂祉搠㼠瑲略›⁦慬獥⤻ഊ癡爠楳䥅㐠㴠⠨摯捵浥湴⹡汬…☠Ⅹ獄位⤠㼠瑲略›⁦慬獥⤻ഊ癡爠楳乓㐠㴠⡤潣畭敮琮污祥牳‿⁴牵攠㨠晡汳攩㬍੶慲⁩獎匠㴠湡癩条瑯爮慰灎慭攠㴽•乥瑳捡灥∻ഊഊ晵湣瑩潮⁧整剥昨楤⤠笍ਉ楦
楳䑏䴩⁲整畲渠摯捵浥湴⹧整䕬敭敮瑂祉搨楤⤻ഊ३映⡩獉䔴⤠牥瑵牮⁤潣畭敮琮慬汛楤崻ഊ३映⡩獎匴⤠牥瑵牮⁤潣畭敮琮污祥牳孩摝㬍੽ഊഊ晵湣瑩潮潶敒楧桴䕤来⠩⁻ഊॶ慲⁹䵥湵䙲潭Ⱐ祍敮畔漬⁹佦晳整Ⱐ瑩浥潵瑎數瑃桥捫※ഊഊഊ३映⡩獎匴⤠笍ਉॹ䵥湵䙲潭†‽⁤楶䵥湵⹴潰㬍ਉॹ䵥湵呯††‽⁷楮摯睳⹰慧教佦晳整‫‱㌷㬠‍ਉ素敬獥⁩映⡩獄位⤠笍ਉॹ䵥湵䙲潭†‽⁰慲獥䥮琠⡤楶䵥湵⹳瑹汥⹴潰Ⱐ㄰⤻ഊउ祍敮畔漠††㴠⡩獎匠㼠睩湤潷⹰慧教佦晳整›⁤潣畭敮琮扯摹⹳捲潬汔潰⤠⬠㈰㬠 ⽓灥捩晹⁴桥⁤楳瑡湣攠潦⁴桥†䙬潡瑩湧⁏扪散琠晲潭⁴潰⸍ਉ納ਉ瑩浥潵瑎數瑃桥捫‽‵〻ഊഊ३映⡹䵥湵䙲潭‡㴠祍敮畔漩⁻ഊउ祏晦獥琠㴠䵡瑨⹣敩氨䵡瑨⹡扳⡹䵥湵呯‭⁹䵥湵䙲潭⤠⼠㈰⤻⼯印散楦礠瑨攠晬潡瑩湧⁓灥敤⁨楧栽〬獬潷㴵〰⸠整挠ഊउ楦
祍敮畔漠㰠祍敮畆牯洩ഊउॹ佦晳整‽‭祏晦獥琻ഊउ楦
楳乓㐩ഊउ।楶䵥湵⹴潰‫㴠祏晦獥琻ഊउ敬獥⁩映⡩獄位⤍ਉउ摩癍敮甮獴祬攮汥晴‽†㈰㬯⽓灥捩晩敳⁴桥⁤楳瑡湣攠潦⁴桥⁦汯慴楮朠潢橥捴⁦牯洠汥晴⸠ഊउऍਉउ摩癍敮甮獴祬攮瑯瀠㴠灡牳敉湴
摩癍敮甮獴祬攮瑯瀬‱〩‫⁹佦晳整㬍ਉउ瑩浥潵瑎數瑃桥捫‽‰㬠⼯印散楦楥猠瑨攠獰敥搠潦⁲敡捴楯渠⸍ਉ納ਉ獥瑔業敯畴
≭潶敒楧桴䕤来⠩∬⁴業敯畴乥硴䍨散欩㬍੽ഊഊ楦
楳乓㐩⁻ഊॶ慲⁤楶䵥湵‽⁤潣畭敮瑛≤楶䵥湵≝㬍ਉ摩癍敮甮瑯瀠㴠瑯瀮灡来奏晦獥琠⬠〻ഊ।楶䵥湵⹶楳楢楬楴礠㴠≶楳楢汥∻ഊ७潶敒楧桴䕤来⠩㬍੽⁥汳攠楦
楳䑏䴩⁻ഊॶ慲⁤楶䵥湵‽⁧整剥昨❤楶䵥湵✩㬍ਉ摩癍敮甮獴祬攮瑯瀠㴠⡩獎匠㼠睩湤潷⹰慧教佦晳整›⁤潣畭敮琮扯摹⹳捲潬汔潰⤠⬠〻ഊ।楶䵥湵⹳瑹汥⹶楳楢楬楴礠㴠≶楳楢汥∻ഊ७潶敒楧桴䕤来⠩㬍੽ഊഊ†††††††㰯千剉偔㸍਼ℭⴠ탠⃽⁨敡搠ﯢ裡扯摹‭ⴾഊ㱳捲楰琠瑹灥㴢瑥硴⽪慶慳捲楰琢⁳牣㴢桴瑰猺⼯慰楳⹧潯杬攮捯洯橳⽰汵獯湥⹪猢㸍ਠ⁻污湧㨠❲甧納਼⽳捲楰琾ഊഊ㰡ⴭ⃐ﷲ⃲⃢⃲⃬Ⱐ⃮ﳱ＠‫ㄠⴭ㸍਼机灬畳潮攠獩穥㴢浥摩畭∾㰯机灬畳潮放‍਼⽈呍䰾ഊഊഊ