Линейные операторы
Векторы , , , , , векторного пространства R3 заданы координатами в некотором базисе { , , }. Линейные операторы и f имеют матрицы А и В соответственно в базисах { , , } и { , , }. Найдите матрицы линейных операторов + f, . f в базисе { , , }, если:
29.01.
= (2; 2; 2),
= (3; 4; 3),
= (5; 5; 6),
= (1; 3; 2),
= (9; 27; 16),
= (7; 22; 14);
29.02.
= (1; 2; 1),
= (–1; –3; –3),
= (–4; –6; 1),
= (1; 0; –3),
= (–1; 2; 3),
= (2; 4; –5);
29.03.
= (2; 2; 2),
= (2; 4; 6),
= (–6;–10;–12),
= (2; –2; 4),
= (–2; 4; 2),
= (4;–2; 16);
29.04.
= (–4; 3; 5),
= (3; –2; –3),
= (–1; 1; 1),
= (–2; 3; 3),
= (1; –1; –1),
= (–1; 0; 1);
29.05.
= (1; 1; 1),
= (1; 2; 3),
= (–3; –5; –6),
= (1; –1; 2),
= (–1; 2; 1),
= (2; 1; 8);
29.06.
= (1; 0; 1),
= (2; –1; 2),
= (0; 2; –2),
= (1; –2; 0),
= (1; 1; 1),
= (–2; 3; 1);
29.07.
= (–1; 1; 0),
= (1; –1; 2),
= (1; 1; 1),
= (2; 2; 3),
= (1; –1; 2),
= (3; 0; 1);
29.08.
= (1; 2; 1),
= (2; 3; 3),
= (–1; 2; –6),
= (2; 3; –1),
= (1; 2; 2),
= (1; 1; –3);
29.09.
= (–1; 0; 1),
= (0; 1; 1),
= (1; 1; 1),
= (–2; 1; 2),
= (1; 2; 2),
= (2; –3; 4);
29.10.
= (1; 2; 0),
= (0; –1; 2),
= (2; 4; 1),
= (1; –1; 0),
= (1; 0; 2),
= (–2; 1;–1);
29.11.
= (1; 0; 1),
= (1; 2; 1),
= (1; 1; 1),
= (0; 0; 1),
= (1; 2; 2),
= (1; 0; 2);
29.12.
= (1; 0; –1),
= (1; 1; –2),
= (1; –1; –1),
= (1; –1; 1),
= (1; 2; 0),
= (0; –2; 1);
29.13.
= (1; 1; 1),
= (1; 2; 1),
= (2; 1; 3),
= (1; 2; –1),
= (–1; –1; 1),
= (1; 3; 0);
29.14.
= (1; 1; 1),
= (2; 0; 2),
= (0; 1; 1),
= (1; 1; 0),
= (1; 3; 1),
= (0; 1; 3);
29.15.
= (1; 1; 2),
= (1; 1; 1),
= (–1; 1; 0),
= (1; 1; –2),
= (3; 0; 1),
= (2; 2; 3);
29.16.
= (1; 0; 0),
= (1; 1; 0 ),
= (1; 0; –1),
= (1; 1; 2),
= (2; 1; 0),
= (2; 2; 3);
29.17.
= (0; 1; –1),
= (2; 1; 1),
= (–1; –1; 0),
= (–1; –2; 3),
= (0; –1; 2),
= (1; 1; –4);
29.18.
= (2; 1; 1),
= (1; 0; 0 ),
= (–1; –1; –1),
= (2; 0; –1),
= (0; 0; 1),
= (–1; 1;–1);
29.19.
= (1; –1; 0),
= (1; 0; –1),
= (2; –1; 1),
= (1; –3; –1),
= (2; 5; –1),
= (0; 1;–1);
29.20.
= (–1; 1; 1),
= (0; 0; –1),
= (2; –1; –1),
= (2; 1; –1),
= (0; –2; 0),
= (1; –1; 1);
29.21.
= (2; –1; 3),
= (0; 0; –1),
= (1; –2; –5),
= (3; 0; –1),
= (1; –1; –2),
= (0; 1; –1);
29.22.
= (–1; 1; 1),
= (0; 1; 1),
= (1; –2; –1),
= (2; –3; 3),
= (–1; 0; –2),
= (0; –3; 1);
29.23.
= (–1; 1; –1),
= (0; 0; –1),
= (2; –1; 1),
= (3; –2; –1),
= (1; –5; –2),
= (0; 1; –1);
29.24.
= (2; 1; –1),
= (0; 1; 0),
= (–2; 1; –1),
= (3; –1; 1),
= (1; 1; 1),
= (0; –4;–2);
29.25.
= (2; –3; –1),
= (1; 1; 1),
= (0; 5; 2),
= (–1; 1; 0),
= (–1; 1; 0),
= (1; –1; 1);
29.26.
= (0; 1; 2),
= (1; 1; –1),
= (2; 1; 3),
= (1; –1; 3),
= (0; –2; 1),
= (2; 2; 5);
29.27.
= (–1; 2; 1),
= (1; –1; 1),
= (0; 1; 3),
= (–1; 2; 2),
= (2; –3; –5),
= (1; 0; 0);
29.28.
= (–1; 0; 1),
= (1; 1; 0),
= (2; 1; –1),
= (2; –3; 0),
= (1; 2; –1),
= (0; 1; 1);
29.29.
= (1; –1; 2),
= (0; 1; –2),
= (2; –3; 3),
= (0; 2; 0),
= (1; 1; –1),
= (2; 1; –1);
29.30.
= (2; –1; 1),
= (1; 1; –1),
= (0; 2; 1),
= (–1; 0; –2),
= (0; 1; 1),
= (2; 1; 0);
29.31.
= (–1; 0; 2),
= (0; 1; –1),
= (2; 1; –3),
= (1; 0; 1),
= (2; –1; 2),
= (–1; 1; 1);
29.32.
= (1; 4; 0),
= (–1; –3; –1),
= (2; 7; 1),
= (2; 1; –1),
= (0; –1; 1),
= (1; 1; –1);
29.33.
= (0; –1; –1),
= (1; 2; 1),
= (3; 5; 2),
= (2; –1; 3),
= (0; 1; 1),
= (1; –1; 1);
29.34.
= (2; 3; 0),
= (1; 2; 1),
= (0; 1; 2),
= (1; 1; –1),
= (1; 2; 1),
= (0; 1; 2);
29.35.
= (1; 0; –2),
= (–2; 1; 0),
= (0; –1; –2),
= (2; 0; –4),
= (2; –1; 0),
= (–6; 1;–4);
29.36
= (1; –2; –1),
= (1; 0; 0),
= (1; 1; 2),
= (–2; 1; 3),
= (–4; –3; 6),
= (–2;–2; 4);