To show that the mapping ϕ : ( a 1 , a 2 , ... , a n ) → ( − a 1 , − a 2 , ... , − a n ) is an automorphism of the group R n under component-wise addition.

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Answer 1

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Chapter 6, Problem 42E

To determine

To show that the mapping ϕ:(a1,a2,...,an)→(−a1,−a2,...,−an) is an automorphism of the group Rn under component-wise addition.

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Answer 2

Question

Chapter 6, Problem 42E

To determine

To show that the mapping ϕ:(a1,a2,...,an)→(−a1,−a2,...,−an) is an automorphism of the group Rn under component-wise addition.

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Answer 3

Question

Chapter 6, Problem 42E

To determine

To show that the mapping ϕ:(a1,a2,...,an)→(−a1,−a2,...,−an) is an automorphism of the group Rn under component-wise addition.

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Answer 4

Question

Chapter 6, Problem 42E

To determine

To show that the mapping ϕ:(a1,a2,...,an)→(−a1,−a2,...,−an) is an automorphism of the group Rn under component-wise addition.

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Answer 5

Chapter 6, Problem 42E

To determine

To show that the mapping ϕ:(a1,a2,...,an)→(−a1,−a2,...,−an) is an automorphism of the group Rn under component-wise addition.

Answer 6

Chapter 6, Problem 42E

To determine

To show that the mapping ϕ:(a1,a2,...,an)→(−a1,−a2,...,−an) is an automorphism of the group Rn under component-wise addition.

Answer 7

Chapter 6, Problem 42E

To determine

To show that the mapping ϕ:(a1,a2,...,an)→(−a1,−a2,...,−an) is an automorphism of the group Rn under component-wise addition.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 6 - Prob. 1E Ch. 6 - Find Aut(Z).Ch. 6 - Let R+ be the group of positive real numbers under...Ch. 6 - Show that U(8) is not isomorphic to U(10).Ch. 6 - Show that U(8) is isomorphic to U(12).Ch. 6 - Prove that isomorphism is an equivalence relation....Ch. 6 - Prove that S4 is not isomorphic to D12 .Ch. 6 - Show that the mapping alog10a is an isomorphism...Ch. 6 - In the notation of Theorem 6.1, prove that Te is...Ch. 6 - Given that is a isomorphism from a group G under...

To show that the mapping ϕ : ( a 1 , a 2 , ... , a n ) → ( − a 1 , − a 2 , ... , − a n ) is an automorphism of the group R n under component-wise addition.

Solution Summary: The author explains that the mapping varphi :(a_1, a

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To show that the mapping ϕ:(a1,a2,...,an)→(−a1,−a2,...,−an) is an automorphism of the group Rn under component-wise addition.

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Chapter 6 Solutions