kindly give a detailed explanation 4: Let F: R² → R2 and G: R2 → R2 be two linear images, and assume that they have thematrices F = (₂) and G² = (²2), with respect to any base v in R². Which is thematrix (G OF) of the composite image G ° F, A, B or C?ABC2(4²)601 53 3232

Answered: Image /qna-images/answer/7ec3b71c-200e-41b2-9e20-3c6593c6fbf9.jpg

Answered: 4: Let F: R² → R² and G: R² → R² be two…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 34E: 34. If is an ideal of prove that the set is an ideal of . The set is called the annihilator of the...

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Prove that the equalities in Exercises hold for all in . Assume only the basic postulates for and those properties proved in this section. Subtraction is defined by .
34. If is an ideal of prove that the set is an ideal of . The set is called the annihilator of the ideal . Note the difference between and (of Exercise 24), where is the annihilator of an ideal and is the annihilator of an element of.
[Type here] 21. Prove that ifand are integral domains, then the direct sum is not an integral domain. [Type here]
Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary elements of and ordered integral domain. If and, then. One and only one of the following statements is true: . Theorem 5.30 Properties of Suppose that is an ordered integral domain. The relation has the following properties, whereand are arbitrary elements of. If then. If and then. If and then. One and only one of the following statements is true: .
Exercise are stated using the notation in the last paragraph of Example. Prove or disprove for all . Example : In this example we outline the development of the quaternions as the set , For each in , we imitate conjugates in and write , It is left as exercise to verify that If , then , and . Thus has all the field properties except commutative multiplication.
Prove that the equalities in Exercises hold for all in . Assume only the basic postulates for and those properties proved in this section. Subtraction is defined by .
Prove that the equalities in Exercises 111 hold for all x,y,zandw in Z. Assume only the basic postulates for Z and those properties proved in this section. Subtraction is defined by xy=x+(y). x0=0

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4: Let F: R² → R² and G: R² → R² be two linear images, and assume that they have the 1 matrices F = (12) and G = (36), with respect to any base y in R². Which is the 0 matrix (Go F) of the composite image G O F, A, B or C? 2 A (1²) 60 B C 15 3 3 2 3 3 2