Solve 3 and 4... Please solve it fast 3. Find two elements a and b in Z25 such that a and b are units, but a +b is not a unit. Justifyyour answer.4. Let I = {a+ bv3 a, beZ and a-b is even}. Show that I is an ideal of Z[V3).

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Answered: 3. Find two elements a and b in Z25…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 26CR: For u=(0,3,13) and v=(43,1,3), a find the inner product represented by u,v=2u1v1+u2v2+2u3v3 and b...

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Similar questions

23. Find all distinct principal ideals of for the given value of . a. b. c. d. e. f.
For u=(0,3,13) and v=(43,1,3), a find the inner product represented by u,v=2u1v1+u2v2+2u3v3 and b use this inner product to find the distance between uandv.
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.
Show that if ax2+bx+c=0 for all x, then a=b=c=0.
aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _
Solve each of the following equations by finding [ a ]1 and using the result in Exercise 9. a.[ 4 ][ x ]=[ 5 ]in13b.[ 8 ][ x ]=[ 7 ]in11c.[ 7 ][ x ]=[ 11 ]in12d.[ 8 ][ x ]=[ 11 ]in15e.[ 9 ][ x ]=[ 14 ]in20f.[ 8 ][ x ]=[ 15 ]in27g.[ 6 ][ x ]=[ 5 ]in319h.[ 9 ][ x ]=[ 8 ]in242 Let [ a ] be an element of n that has a multiplicative inverse [ a ]1 in n. Prove that [ x ]=[ a ]1[ b ] is the unique solution in n to the equation [ a ][ x ]=[ b ].
Express (AB)(AB) in terms of unions and intersections that involve A,A,B,andB
5. Show that 1+a 1 1 1 1+b 1 1 1 1+c =abc + ab +ac + bc.

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3. Find two elements a and b in Z25 such that a and b are units, but a +b is not a unit. Justify your answer.