PROBLEM 1 1.1 Let S CR2. Write down the definition of a symmetry of S. 1.2 Let G = Z/14Z. What is the order of the element [4] Є G? Does this element generate G? 1.3 What does it mean for a matrix A Є M₂(R) to be orthogonal? If A is orthogonal and det(A) = 1, what does A represent geometrically? No explanation is required. 1.4 Give an example of a subset SCR² for which the group E2(S, R) is finite but not abelian. No explanation is required.
PROBLEM 1 1.1 Let S CR2. Write down the definition of a symmetry of S. 1.2 Let G = Z/14Z. What is the order of the element [4] Є G? Does this element generate G? 1.3 What does it mean for a matrix A Є M₂(R) to be orthogonal? If A is orthogonal and det(A) = 1, what does A represent geometrically? No explanation is required. 1.4 Give an example of a subset SCR² for which the group E2(S, R) is finite but not abelian. No explanation is required.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 5AEXP
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![PROBLEM 1
1.1 Let S CR2. Write down the definition of a symmetry of S.
1.2 Let G = Z/14Z. What is the order of the element [4] Є G? Does this element
generate G?
1.3 What does it mean for a matrix A Є M₂(R) to be orthogonal? If A is orthogonal
and det(A) = 1, what does A represent geometrically? No explanation is required.
1.4 Give an example of a subset SCR² for which the group E2(S, R) is finite but not abelian.
No explanation is required.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf4d5614-e5fa-4399-aabc-c345eeef0588%2Faf0e600c-b037-4b28-8e28-efa8d9ee7e80%2Fushqso_processed.png&w=3840&q=75)
Transcribed Image Text:PROBLEM 1
1.1 Let S CR2. Write down the definition of a symmetry of S.
1.2 Let G = Z/14Z. What is the order of the element [4] Є G? Does this element
generate G?
1.3 What does it mean for a matrix A Є M₂(R) to be orthogonal? If A is orthogonal
and det(A) = 1, what does A represent geometrically? No explanation is required.
1.4 Give an example of a subset SCR² for which the group E2(S, R) is finite but not abelian.
No explanation is required.
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