LISTA1 P1 AL
871 palavras
4 páginas
Universidade Federal do Esp´ırito Santo´
Lista de exerc´ıcios de Algebra
Linear - MAT09592
Quest˜oes do livro texto:
Se¸
c˜ ao 1.1: 2, 3, 6, 9, 10, 12, 14, 15, 17, 18, 22, 23, 24, 25, 26, 28, 29, 32, 33, 34
Se¸
c˜ ao 1.2: 2, 3, 5, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 24, 27, 28, 29, 31, 32, 33
Se¸
c˜ ao 1.3: 1, 4, 5, 7, 10, 11, 12, 14, 15, 19, 21, 22, 23, 24, 25, 26, 32
Se¸
c˜ ao 1.4: 1, 2, 4, 5, 8, 10, 11, 12, 13, 14, 15, 17, 19, 22, 23, 24, 25, 28, 29, 31, 32, 33, 34, 36
Se¸
c˜ ao 1.5: 2, 5, 6, 7, 10, 11, 12, 13, 14, 16, 17, 19, 21, 23, 24, 26, 27, 28, 29, 32, 34, 37, 38, 39, 40
Se¸
c˜ ao 1.7: 1, 3, 6, 8, 9, 13, 15, 17, 19, 21, 22, 23, 24, 25, 27, 28, 30, 32, 33, 36, 38, 39, 40
Se¸
c˜ ao 1.8: 1, 4, 6, 7, 10, 12, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 31, 32, 34, 36
Se¸
c˜ ao 1.9: 2, 3, 5, 6, 9, 10, 11, 13, 14, 16, 17, 20, 21, 23, 24, 25, 26, 29, 30, 31, 34, 36
Se¸
c˜ ao 2.1: 2, 4, 6, 8, 10, 11, 13, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 28, 32, 34
Se¸
c˜ ao 2.2: 4, 7, 9, 10, 14, 15, 16, 20, 24, 28, 32, 33, 34, 35
Se¸
c˜ ao 2.3: 2, 4, 7, 11, 12, 16, 18, 20, 21, 23, 26, 27, 28, 30, 32, 34, 35, 36, 38
Se¸
c˜ ao 2.4: 2, 5, 7, 8, 9, 11, 12, 13, 21, 22
Se¸
c˜ ao 2.8: 2, 4, 6, 7, 10, 12, 14, 17, 20, 21, 22, 24, 26, 29, 30, 31, 32, 36
Se¸
c˜ ao 2.9: 1, 2, 4, 5, 6, 8, 11, 12, 13, 14, 15, 17, 18, 20, 23, 27, 28
Mais exerc´ıcios:
3
1
5 −2 0
−7
−2
9 −5 , b = 9 e p =
1. Sejam A = −3 1
0 .
4 −8 −1 7
0
−4
(a) O sistema Ax = b tem solu¸ca˜o u
´nica?
(b) Pode-se mostrar que p satisfaz a equa¸ca˜o matricial Ax = b. Exiba b como uma combina¸ca˜o linear das colunas de A.
T
T
2. Sejam K, L, M matrizes 3 × 1. Uma matriz A satisfaz AK = 1 1 1 , AL = 0 1 −1 ,
T
AM = −1 2 −3 . Mostre que A tem inversa e calcule essa inversa em fun¸c˜ao de K, L, M .
Sugest˜ao: considere a matriz B com colunas K, L, M e calcule o produto AB.
1 −1 0
1 . Defina a transforma¸c˜ao linear T (x) = Ax.
3. Seja A = 0 2
3 −7 −2
(a) O sistema