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```Lista de A´lgebra Linear 2 \u2014 10.1
(1) Calcule o nu´cleo e imagem das matrizes (escreva uma base e suas equac¸o\u2dces)
(a) (
2 3 5 7
3 7 11 17
)
(b) \uf8eb\uf8ec\uf8ec\uf8ed
2 3
5 3
7 11
13 17
\uf8f6\uf8f7\uf8f7\uf8f8
(c) \uf8eb\uf8ec\uf8ec\uf8ed
3 \u22121 \u22121 \u22121
\u22121 3 \u22121 \u22121
\u22121 \u22121 3 \u22121
\u22121 \u22121 \u22121 3
\uf8f6\uf8f7\uf8f7\uf8f8
(2) Ache equac¸o\u2dces para o subespac¸o de V \u2286 R8 gerado por (1, 1, 1, 1, 1, 1, 1, 1),
(1,\u22121, 1,\u22121, 1,\u22121, 1,\u22121), (1, 0,\u22121, 0, 1, 0,\u22121, 0), (0, 1, 0,\u22121, 0, 1, 0,\u22121),
(\u22127,\u22125,\u22123,\u22121, 1, 3, 5, 7).
(3) Ache uma base para o subespac¸o W \u2286 R7 definido pelas equac¸o\u2dces
x1 + x2 + x3 + x4 + x5 + x6 + x7 = 0, 3x1 + 2x2 + x3 \u2212 x5 \u2212 2x6 \u2212 3x7 = 0.
(4) Encontre uma base para V \u2229W \u2286 R6 onde
V = \u3008(0, 1, 1, 2, 3, 5), (1, 2, 3, 4, 5, 6), (2, 3, 5, 7, 11, 13), (0, 1, 4, 9, 16, 25)\u3009,
W = \u3008(1, 1, 1, 1, 1, 1), (2,\u22121,\u22121, 2,\u22121,\u22121), (\u22121, 2,\u22121,\u22121, 2,\u22121), (1,\u22121, 1,\u22121, 1,\u22121)\u3009.
1```