(6) ≤a) Determine the following groups:Homz(Q, Z),Homz(Q, Q),Homz(Q/Z, Z)for n E N.Homz(Z/nZ, Q)b) Show for ME MR: HomR (R, M) = M.

Approach to solving the question:Part (a): Determine the following groupsHomZ(Q,Z):This represents…

Answered: (6) ≤ a) Determine the following…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 64E

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Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
22. Find the center for each of the following groups . a. in Exercise 34 of section 3.1. b. in Exercise 36 of section 3.1. c. in Exercise 35 of section 3.1. d., the general linear group of order over. Exercise 34 of section 3.1. Let be the set of eight elements with identity element and noncommutative multiplication given by for all in (The circular order of multiplication is indicated by the diagram in Figure .) Given that is a group of order , write out the multiplication table for . This group is known as the quaternion group. Exercise 36 of section 3.1 Consider the matrices in , and let . Given that is a group of order 8 with respect to multiplication, write out a multiplication table for. Exercise 35 of section 3.1. A permutation matrix is a matrix that can be obtained from an identity matrix by interchanging the rows one or more times (that is, by permuting the rows). For the permutation matrices are and the five matrices. Given that is a group of order with respect to matrix multiplication, write out a multiplication table for .
Explain thedetermine
5. (a). u. (7v+w); (b). (uw)w||; (c). ||u|| (vw); (d). (uv). w. Let & (1, 2, 0), 7(4, 1, -2), and w= (0, 2,3). Find
2. Let A = {a, b, c}, B = {x, y, z},C = {r, s, t}. Let f : A → B and g : B → C be defined by: f = {(a, x), (b, z), (c, x)}, and g = {(x, t), (y,r), (z,r)}. Find (a) Composition function gof : A→ C (b) Range of f, Range of g, Range of go f.
- Let u = (9, 9, 8) and = ( − 9, -1, - 8). Find proj; (u).
Let u == (7,5,-5) and = (−1, −2, 2). Compute the following: u v . . = 2 7(ū. v) = (7) · v = ū. (77) = ( ñ · v ) v =
Let f(x, y) = In(x²y³), where a = s2 + t² and y = 2s + 3t. %3D Which of the following is a correct representation for ? as O af (군E) (20)+ (2) 2s + 3t %3D ds s2+ t2 fe 2 3 Gi) (2t) + (3) 2s + 3t %3D ds s2 + t2 fe 2 3 ds s2 + t2 2s + 3t o af (2) 3 (2s + 2t) + (5) 2s + 3t as s2 +
Let f(x, y) = In(x²y³), where r = s2 + t2 and y = 2s + 3t. Which of the following is a correct representation for ? as O af )(2) (2s)+ %3D as g2 + t² 2s + 3t O af -) (2t) + s2 +t2 ) (3) as 2s + 3t O af as 2. s2 + t2 2s + 3t O af s2 + t2 (2s + 2t) + (5) 2s +3t ds 3. 3 2)

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(6) ≤ a) Determine the following groups: Homz(Q, Z), Homz(Q, Q), Homz(Q/Z, Z) for n E N. Homz(Z/nZ, Q) b) Show for ME MR: HomR (R, M) = M.