Q18picture 2 is the general answer key. Do not use the table on the answer key. write speific steps for this question to prove it is under operation and it is a group pdfQ 山☆K Paused17 / 22|129%Inverse: The product property 1-UC(1,)–de( 7A A)–Uet(A )*Uet(A showsthat if det(4) = 1, then det(A-) = 1 also.Copyright O 2021 Pearson Education, Inc.2. Groups9.18. Matrix multiplication is associative, so it remains to show that G is closed undermatrix multiplication, G has an identity and each element of G has an inverse. The*e atable for G isefrom which all of these properties are easily spotted.eaaeb beaWe must show that S is closed under *, that is, that a+b+ab±-1 for a,be S. Now a + b + ab = –1 if and only if 0 = ab+ a+b+1= (a+1)(b+1). This isthe case if and only if either a = -1 or b = -1, which is not the case for a, bɛ S.19. а.b. Associative: We havea * (b * c)= a * (b+c+bc)% = a + (b+c+ bc)+a(b+c + bc) = a +b+c + ab + ac + bc + abcMacBook ProSearch or type URL&*.. S GaUnG de土 DoSo00000000000..O ☆ 司olatform.virdocs.com/r/s/0/doc/1559577/sp/165492540/mi/542334716?cfi=%2F4%2F2%Sa groupb. Show that (nZ, +) ~ (Z, +).28In Exercises 11 0 through 180, determine whether the given set of matrices under the specified operation,matrix addition or multiplication, is a group. Recall that a diagonal matrix is a square matrix whose onlynonzero entries lie on the main diagonal, from the upper left to the lower right corner. An upper-triangularmatrix is a square matrix with only zero entries below the main diagonal. Associated with each n x n matrixA is a number called the determinant of A, denoted by det(A). If A and B are both n x n matrices, thendet (AB) =det (A) det (B). Also, det(In) = 1 and A is invertible if and only if det (A) +0.11. All n x n diagonal matrices under matrix addition.12. All n x n diagonal matrices under matrix multiplication.13. All n x n diagonal matrices with no zero diagonal entry under matrix multiplication.14. All n x n diagonal matrices with all diagonal entries 1 or –1 under matrix multiplication.15. All n x n upper-triangular matrices under matrix multiplication.16. All n x n upper-triangular matrices under matrix addition17. All n x n upper-triangular matrices with determinant 1 under matrix multiplication.1V32, and118. The set of 2 × 2 matrices G = {e, a, b} where e =a =V321V3b =2under matrix multiplication.V31219. Let S be the set of all real numbers except -1. Define * on S by人MacBook ProG Search or type URL%23&368.9.ETYSFGJK L+Rw/

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Copyright 2021 Pearson Education, Inc. 2. Groups 18. Matrix multiplication is associative, so it remains to show that G is closed under matrix multiplication, G has an identity and each element of G has an inverse. The e a b table for G is e b from which all of these properties are easily spotted. e a a a e b b e a 19. a. We must show that S is closed under *, that is, that a+b+ab -1 for a, beS. Now a + b+ ab = -1 if and only if 0 = ab+ a+b+1= (a+1)(b+1). This is the case if and only if either a =-1 or b =-1, which is not the case for a, be S. b. Associative: We have a * (b *c) = a * (b+c+bc) = a + (b+c+ bc)+ a(b+c+ bc) = a+b+c+ ab+ ac + be + abc MacBook Pro G Search or type URL

Copyright 2021 Pearson Education, Inc. 2. Groups 18. Matrix multiplication is associative, so it remains to show that G is closed under matrix multiplication, G has an identity and each element of G has an inverse. The e a b table for G is e b from which all of these properties are easily spotted. e a a a e b b e a 19. a. We must show that S is closed under , that is, that a+b+ab -1 for a, beS. Now a + b+ ab = -1 if and only if 0 = ab+ a+b+1= (a+1)(b+1). This is the case if and only if either a =-1 or b =-1, which is not the case for a, be S. b. Associative: We have a (b c) = a (b+c+bc) = a + (b+c+ bc)+ a(b+c+ bc) = a+b+c+ ab+ ac + be + abc MacBook Pro G Search or type URL

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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