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554-HW-2q - Homan and Kunze Linear Algebra MA 530 HW 2 p40...

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Hoffman and Kunze - Linear Algebra MA 530 - HW 2: p40/ 5,7,8,9; p48/ 7,8,9,13; p54/ 1,3; p66/ 3, 7 p40, 7 We have subspaces W 1 , W 2 V , for V a vectorspace, such that W 1 W 2 is a subspace of V . Show one of W 1 , W 2 is contained in the other. p40, 8 V is the vectorspace of all functions from R into R . Let V e be the subset of V of all even functions and V o the subset of all odd functions. Show (a) each is a subspace of V , (b) V e + V o = V , and (c) they have trivial intersection. p40, 9 Let W 1 and W 2 be subspaces of V such that V = W 1 + W 2 and W 1 W 2 = { 0 } . Prove for each vector v V that there are unique vectors a W 1 and b W 2 such that v = a + b . p48, 8 Find a basis { A 1 , A 2 , A 3 , A 4 } for F 2 × 2 such that each A i satisfies A 2 i = A i . p48, 9 Given: x, y, z are linearly independent vectors in V a vectorspace. Show that ( x + y ) , ( y + z ) , ( z + x ) are also linearly independent in V , a vectorspace over C . p48, 13 Let V be a vectorspace over F 2 . Given: x, y, z are linearly independent vectors in V . Discuss whether
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