2. for the given matrices A = -3 9 14 7 9 -17 -8 Find : a. A + D b. AA + DDT C. BC d. (AB + AD) T e. 3A + 4D 1 13 " B= 15 - 2 -9 5 1 12 " C = 4 5 -7 11 D = 18 3 21 4 8 5 -6 0 34

Q: (2) Chapter 6, exercise 7.11: Prove that the only subgroup of order 12 of the symmetric group S₁ is…

A: We know that A4 is subgroup S4 of order 12  We have to show that A4 is only subgroup of S4 of order…

Q: (a) log, 10 - log, 7 = log, (b) log, 11 + log,U- log, 77 (c) log, 25 2 logs

A:

Q: Let V₁ = -[---[- 3 the subspace W spanned by {V₁, V2, V3, V4). V2 and v₁ = [4] 9 Find a basis for

A: Row Reduce Echleon form

Q: For the given vectors u andi, find the value of u v and normalize 1. u = (2,7,–1,20), 2. ü = (3,…

A: The dot product and addition of two vectors is given by Given…

Q: 27. Payton ran l miles on Monday, 2 miles on 7. miles on Wednesday. What is the 8. Tuesday, and 1-…

A: topic -median of distance median is the value in the middle when data is arranged in ascending or…

Q: one Prove Property the flig statements property li Ans is true by reordening to form a proofr A, BV…

A: Given: V=M3×3 and two matrices  A,B∈M3×3 .There is some statements also given , (A) Assume that A…

Q: B = Solve for X the matrix equation 2XTA= B, where A = 11 1 and -1₁ [8 -6]

A:

Q: 6) Chapter 7, exercise 4.1: The icosahedral group operates on the set of five inscribed cubes in the…

A: Given: The icosahedral group operates on the set of five inscribedcubes in the dodecahedron. To…

Q: Prove that H= {(s, t, 0) |s and t are real numbers} is a subspace of R^3. (1

A:

Q: Chapter 2, exercise 10.2(a): Let H and K be subgroups of a group G. Prove that the intersection…

A:

Q: If S is a subring of a ring R, then S[a] is a subring of R[x]. Exercise 2.35.1 Prove this assertion!…

A:

Q: 1 0 0 0 0 1 2 -6 2 -8 10 1 0 1 0 3 -2 -5 -16 |

A: We have to multiply: 1000012-60010003-22-8-5-16

Q: 4 1 [1 -1 2] [2 3] +|0 1

A: Given matrix expression: 1-12 4-10 23 + 1001-1-1

Q: Exercise 2.114 Consider the ring Q[/m] of Example 2.12. Now assume for this exercise that m is not a…

A:

Q: Find the Four Fundamental Subspaces of the matrix A of size 4 by 1 given below: -2 1 0 Note: Also…

A:

Q: Given the subspace H a- -4b-2c 2a + 5b-4c -a +2c -3a+7b+6c a) Find a matrix A such that H = Col A.…

A: Given subspace is the following :Now for any reals  (say),a) Then So

Q: 210. 153 How many abelian groups of order n = Explain your reasoning. You may assume that the data…

A:

Q: Chapter 6, exercise 4.2(b): List the proper normal subgroups N of the dihedral group D₁ and identify…

A:

Q: 1- Let G = (U15, ×), and let N = , the subspace generated by 2. List all the right cosets of N, and…

A:

Q: (3) Let p be a prime number. Let G be the set of matrices of the form (7) 01 (x, y, z = Z/Zp). 0 1…

A:

Q: Given the description, write the quadratic FUNction. 3) The graph of x shifted to the left 11 and up…

A:

Q: Without using the structure theorem for finite abelian groups, prove that a finite abelian group has…

A: Given: Let G be a finite abelian group. To prove: G has an element of order p, for every prime…

Q: Suppose you randomly choose a card from the first deck, add it to the second deck and then randomly…

A: Let us define some events A : ace is added to second deck. B : a king is added to second deck. C : a…

Q: (1) Use the counting formula to determine the orders of the group G of rotational sym- metries of a…

A:

Q: Let G be a group. Let x,y e G be such that O(x) = 4, O(y) = 2, x^3 y = yx. Then O(xy) is 6. Infinity…

A:

Q: 2. Let p and q be two distinct prime numbers. Compute the order of U (pq). Use this result to…

A: We have to solve given problem:

Q: 7- Let G = U15, and let K = {1, 4}, then K is a subgroup of G. List the elements of G/K, and find…

A:

Q: Given A and b in Exercises 11 and 12, write the augmented matrix for the linear system that…

A:

Q: 4.2. An nth root of unity is a complex number z such that z" = 1. (a) Prove that the nth roots of…

A:

Q: Which ordered pairs should be removed to make the graph a function?

A:

Q: In which of the following cases is H a subgroup of G? (a) G GLn (C) and H = GLn(R). (b) G = RX and H…

A: Subgroup-: Let H be a non empty subset of a group G then H is said to be subgroup of G if H is…

Q: The first four Hermite polynomials are 1,2t,−2+4t²,−12t + 8t³ and arise as solutions to certain…

A: Given, a set It is required to solve the following:a) Show that  is a basis for , the vector space…

Q: In the following system 12x1 + 11x2₂ +10x3 = 9 8x1 + ax2 + 6x3 4x1+3x2+2x3 b, determine the values…

A:

Q: Proilem 2 Let V,w E R' be any two veitors. Write aut. I ūxW ľ in component form, assuming and show…

A:

Q: Exercise 2.46.1 Let R be a commutative ring. Suppose that every nonzero element in R is invertible.…

A: