(c) The following matrix represents the adjacency matrix of a directed graph consisting of six vertices - a, b, c, d, eand f.[2]a b c d efa (0 1 0 0 0 1b1 0 11.c|011 1 0A =d|00 010 0 0f10 0 01e| 01Draw the graph from the adjacency matrix.

Grpah Theory: draow the directed grapyising adjacency matrix

Answered: (c) The following matrix represents the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 69EQ

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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 .
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.
Illustrate the result of exercise 25 using the matrice A=[100020003], B=[1171010810181217] P=[110212111], P1=[112012123] where B=P1AP.
The following is an adjacency matrix for a graph: ? = [0 1 1 01 0 2 11 2 0 10 1 1 1]Answer the following questions by examining the matrix and its powers only, not bydrawing the graph:a) How many walks of length 2 are there from v2 to v3?b) How many walks of length 2 are there from v3 to v4?c) How many walks of length 3 are there from v1 to v4?d) How many walks of length 3 are there from v2 to v3?
Given the following adjacency matrix: v1 v2 v3 v4 M = ⌈ 1 1 2 0 ⌉ v1 | 0 0 1 0 | v2 | 0 0 1 1 | v3 ⌊ 1 2 0 1 ⌋ v4 A. Determine the corresponding graph. 2. Determine the matrix that will give the number of all paths with length two (i.e., compute M2; you must show ALL work!).
Draw the multigraph G whose adjacency matrix A is AG= 0 1 2 0 1 1 1 0 2 1 0 0 0 1 0 1
In R3 find a projection matrix P that represents the projection onto the line through the origin given by x = at, y = bt, z = ct.

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(c) The following matrix represents the adjacency matrix of a directed graph consisting of six vertices - a, b, c, d, e and f. a bcdef a (0 1 0 00 b1 0 10 1 0 1 0 c0 0 A : d 0 0 0 0 1 1. 0 0 0 0 0 1 0 e| 0 1 f1 0 Draw the graph from the adjacency matrix.