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2. Which of the following maps are homomorphisms? If the map is a homomorphism, what is the kernel? a. 6: R* → GL₂(R) defined by b. : R→GL2(R) defined by (a) = - (12) 0 φ(α) = 1 (²₂9)

2. Which of the following maps are homomorphisms? If the map is a homomorphism, what is the kernel? a. 6: R* → GL₂(R) defined by b. : R→GL2(R) defined by (a) = - (12) 0 φ(α) = 1 (²₂9)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 3E: 3. For each of the following mappings, write out and for the given and, where.
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Parts (b,c,d,e) please

2. Which of the following maps are homomorphisms? If the map is a homomorphism, what is the kernel? a. : R* → GL₂(R) defined by b. : R→GL2(R) defined by c. : GL₂(R) → R defined by d. : GL₂(R) → R* defined by e. : M₂(R) → R defined by = (1 2) 0 o(a) = 1 o(a) = = (₁9) * ((a $)). =a+d a 6 ¹ ((ª $)) = ad - bc ø ((a d)) = 6, where M₂ (R) is the additive group of 2 × 2 matrices with entries in R.
Transcribed Image Text:2. Which of the following maps are homomorphisms? If the map is a homomorphism, what is the kernel? a. : R* → GL₂(R) defined by b. : R→GL2(R) defined by c. : GL₂(R) → R defined by d. : GL₂(R) → R* defined by e. : M₂(R) → R defined by = (1 2) 0 o(a) = 1 o(a) = = (₁9) * ((a $)). =a+d a 6 ¹ ((ª $)) = ad - bc ø ((a d)) = 6, where M₂ (R) is the additive group of 2 × 2 matrices with entries in R.
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