QUESTION 23For the directed graph shown below, determine the reachabi ity matrix.O.O a. [1 10 1:1 1 0 11 1 0 11 1 0 11 1 1 10 0 0 0Ob.1 1 1 111 11 a.Г 1 1 0 11 1 0 11 1 0 11 101b.Г 1 1 1 10 0 0 01 1 1 11 1 1 1Ос.ГО 1 1 10 1 1 10 1 1 10 1 1 1Od.Г 1 1 1 11 1 1 10 0 0 01 1 1 1

Answered: QUESTION 23 For the directed graph…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 42EQ

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The gray square in Table 1 has the following vertices: [00],[10],[11],[01] Apply each of the three transformations given in Table 1 to these vertices and sketch the result to verify that each transformation has the indicated effect. Use c=2 in the expansion matrix and c=1 in the shear matrix.
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 .
Exercises 1. Express each permutation as a product of disjoint cycles and find the orbits of each permutation. a. b. c. d. e. f. g. h.
Show that the matrix below does not have an LU factorization. A=0110
For each of the following matrices A in SL(2,R), list the elements of A and give the order | A |. a. A=[ 0111 ] b. A=[ 1110 ]

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QUESTION 23 For the directed graph shown below, determine the reachabi ity matrix. O. O a[110 1 1 10 1 1 1 0 1 1 10 1