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Consider the following functions. (a) f: R*→ GL2 (R), f(a) = 1) (b) ƒ: R* → GL₂ (R), f(a) = (i). a (c) f: GL₂(R)→R,ƒ (d) f: GL₂(R)→ R, f (e) f: GL₂(R) → +R*, ƒ ((ad)) f For each of these functions, answer the following questions, with a (brief) justifi a *((d)) ab. =a+d. = ad-bc.

Consider the following functions. (a) f: R*→ GL2 (R), f(a) = 1) (b) ƒ: R* → GL₂ (R), f(a) = (i). a (c) f: GL₂(R)→R,ƒ (d) f: GL₂(R)→ R, f (e) f: GL₂(R) → +R*, ƒ ((ad)) f For each of these functions, answer the following questions, with a (brief) justifi a *((d)) ab. =a+d. = ad-bc.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the following functions. (a) f: R*→ GL2 (R), f(a) = (89) (1) a (b) f: R*→ GL₂ (R), f(a) = f: f (c) ƒ: GL₂(R) → R‚ ƒ ((ad)) ((" :)) *((*2)) (d) f: GL₂(R) → R, f (e) f: GL₂(R)→ R*, f = ab. (i) Is f a homomorphism? (ii) Is f injective? (iii) Is f surjective? =a+d. = ad-bc. For each of these functions, answer the following questions, with a (brief) justifi- cation.
Transcribed Image Text:1. Consider the following functions. (a) f: R*→ GL2 (R), f(a) = (89) (1) a (b) f: R*→ GL₂ (R), f(a) = f: f (c) ƒ: GL₂(R) → R‚ ƒ ((ad)) ((" :)) *((*2)) (d) f: GL₂(R) → R, f (e) f: GL₂(R)→ R*, f = ab. (i) Is f a homomorphism? (ii) Is f injective? (iii) Is f surjective? =a+d. = ad-bc. For each of these functions, answer the following questions, with a (brief) justifi- cation.
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