(c) The following matrix represents the adjacency matrix of a directed graph consisting of six vertices - a, b, c, d, eand f.[2]a bcdea (0 1 0 0 0 161010 1 0c0 0 1 1 1 0do 0 0 0 1 0e0 0 1 000f1 0 0 0 10A =Draw the graph from the adjacency matrix.

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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 70EQ

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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.
Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.
The adjacency matrix of the graph is __________ 0 1 1 1 0 1 1 1 0 b. 1 0 0 0 1 1 0 0 1 c. 0 0 0 0 0 0 0 0 0 d. 1 1 1 1 1 1 1 1 1
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!).
Suppose A is a matrix. Let B be given by switching two of the rows of A. What is the relation between det(A) and det(B) ?
What should k be for the matrix given in the question to be invertible?
1. determine the type of graph of the figure 2.solve for the adjacency matrix of the given
Consider the adjacency matrix for a graph that is shown below. Answer the following questions by examining the matrix and its powers only, not by drawing the graph. Show your work in a way that makes your reasoning clear. (a) How many walks of length 2 are there from v1 to v3? (b) How many walks of length 3 are there from v1 to v2?

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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. (2] a bc de f a (0 10 0 0 1 610 10 1 0 c0 0 1 1 1 0 A = do 0 0 0 1 0 e0 0 10 0 f1 0 0 0 10 Draw the graph from the adjacency matrix.