5. Let V = {ax¹ + (b − c)x² + 3ax +c+2b: a, b, c ≤ R} ≤ P4. Construct an isomorphism from V to R³. Hint: Use Theorem 1.6.7 (p. 27) and the box in sec. 1.3.3 (p. 15). Make sure to justify if you state that something is a basis.
5. Let V = {ax¹ + (b − c)x² + 3ax +c+2b: a, b, c ≤ R} ≤ P4. Construct an isomorphism from V to R³. Hint: Use Theorem 1.6.7 (p. 27) and the box in sec. 1.3.3 (p. 15). Make sure to justify if you state that something is a basis.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .
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