please send complete handwritten solution only handwritten solution accepted Problem 1. We consider the set G of 3 x 3 matrices with coefficients in Z2 defined as follows:1 a b{| a, b, ce Z,.G :=01c0 0 1(a) Show that G is a subgroup of GL3(Z2). What is its order?(b) Show that the following two elements A, B EG do not commute:A :=B:= 0 ī īIs G a cyclic group?(c) Show that G is generated by A and B.

Answered: Image /qna-images/answer/3993eec7-8662-4361-9a04-2f58c7da83e2.jpg

Answered: We consider the set G of 3 x 3 matrices…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 5AEXP

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Here is a data matrix for a line drawing: D=[012100002440] aDraw the image represented by D. bLet T=[1101]. Calculate the matrix product TD, and draw the image represented by this product. What is the effect of the transformation T? cExpress T as a product of a shear matrix and a reflection matrix. See Problem 2. 2. Verify that multiplication by the given matrix has the indicated effect when applied to the gray square in the table. Use c=3 in the expansion matrix and c=1 in the shear matrix. T1=[1001] Reflection in yaxis T2=[100c] Expansion or contraction in ydirection T3=[10c1] Shear in ydirection
Consider the matrices R=[ 0110 ] H=[ 1001 ] V=[ 1001 ] D=[ 0110 ] T=[ 0110 ] in GL(2,), and let G={ I2,R,R2,R3,H,D,V,T }. Given that G is a group of order 8 with respect to multiplication, write out a multiplication table for G. Sec. 3.3,22b,32b Find the center Z(G) for each of the following groups G. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1. Find the centralizer for each element a in each of the following groups. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1 Sec. 4.1,22 22. Find an isomorphism from the octic group D4 in Example 12 of this section to the group G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of Section 3.1. Sec. 4.6,14 14. Let G={ I2,R,R2,R3,H,D,V,T } be the multiplicative group of matrices in Exercise 36 of section 3.1, let G={ 1,1 } under multiplication, and define :GG by ([ abcd ])=adbc. Assume that is an epimorphism, and find the elements of K= ker . Write out the distinct elements of G/K. Let :G/KG be the isomorphism described in the proof of Theorem 4.27, and write out the values of .
Find a basis for and the dimension of the null space of the given matrix. (problem 32 on picture)
1. What is the dimension of the given matrice? 1 4 -1 2 A= 0 2 3 -6 1 1 9 5 2. Identify element a34, a13 and a22 of the elemnt of matrix A in problem. 3. Define the term identity matrix. a) All terms are one. b) Ones on one of the diagonals and zeros elsewhere. c) Ones on the first rowand column and zeros elsewhere. d) Ones on the main diagonal and zeros elsewhere. 4. Find matrix A so that the following equality is satisfied. A + [2 -3] = [4 2] [4 0] [1 7]
Question 16: Classify the definiteness of the quadratic form associtated to the given matrix:
For Question 3 of task one it states that the transformation matrix for this opertator is invertible. It is not however, this is singular. Does that change Q3 on task 1?
Question 1 Describe the following matrices: 1. Square 2. Diagonal 3. Zero Question 2 Ronamart needs 1000 coffee makers per year. The cost of each coffee maker is $78. Ordering cost is $100 per order. Carrying cost is $20 of unit cost. Lead time is 5 days. RonaMart is open 360 days/yr. Required: 1. What is EOQ model? 2. how many times per year does the store reorder? 3. What is the length of order cycle? 4. What is the total annual cost if EOQ Quantity is ordered?
In the given question find an elementary matrix E such that B=EA.
The following problem refers to a closed Leontief model. Suppose the technology matrix for a closed model of a simple economy is given by the following. P M H A = 0.5 0.1 0.3 0.1 0.3 0 0.4 0.6 0.7 Products Machinery Households Find the gross productions for the industries. (Let H represent the number of household units produced, and give your answers in terms of H.) products units machinery units households units
The following problem refers to a closed Leontief model.Suppose the technology matrix for a closed model of a simple economy is given by the following. P M H A = 0.5 0.1 0.8 0.1 0.3 0 0.4 0.6 0.2 Products Machinery Households Find the gross productions for the industries. (Let H represent the number of household units produced, and give your answers in terms of H.) products 1.53H units machinery .23H units households H units
d) A square matrix with the characteristic polynomial λ5 − 3λ4 − 2λ3 + 5λ2 − 4λ + 2 is invertible (attached in image). True or false. e) If A and B are similar then both of them are diagonalizable. True or false.

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