O 1 1 1]1 1 0 01 10 11 1 1 0Question 4 Let M be the following matrix of a directedgraph1. Draw a diagram of directed graph.2. Find a similar interpretation for the values of the non-diagonal enteriesof MT M.3. Соmpute M"м.

Given that M=0111110011011110. 1 The diagram of the directed graph is given below

Answered: Question 4 Let M be the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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III. Consider the directed graph described by the following:(a) Draw the graph.(b) Find a directed path from vertex 3 to vertex 6.(c) Find a directed cycle starting from and ending at vertex 4.(d) Find the adjacency matrix of the graph.(e) Does there exist a directed path from vertex 2 to vertex 6?
The following augmented matrices represent different Inear systems In x, y, z_Which of the linear systems has a unlque solution? 3 30 90 120 1 10 30 40 2 20 60 80 1253 0134 0011 12 15 15 A. в. C. 11 13 14 1 02 1
34 Identify the adjacency matrix for the given graph. a b Multiple Choice [0 1 1 1 1001 1 0 0 1 1 1 1 0 го о о 17 0 1 1 0 0 1 1 0 [1 0 0 0] [1 1 1 07 1 0 0 1 1 0 0 1 0 1 1 1 [1 0 0 0] 0 1 1 0 0 1 1 0 0001
Solve A part only
1 4 6 8) 10 a. Construct the adjacency matrix. Why is it a block-diagonal matrix? b. Construct the adjacency matrix of its two projections, on the purple and on the green nodes, respectively. c. Calculate the average degree of the purple nodes and the average degree of the green nodes in the bipartite network. d. Calculate the average degree in each of the two network projections. Is it surprising that the values are different from those obtained in part e? 3.
(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 b c d ef a (0 1 0 0 0 1 b1 0 1 1. c|0 1 1 1 0 A = d|0 0 0 1 0 0 0 f10 0 01 e| 0 1 Draw the graph from the adjacency matrix.
1.28 Show that the nonzero rows of an echelon form matrix form a linearly indepen- dent set.
Use powers of adjacency matrices to determine the number of paths of th e specified length between the given vertices length length 3, v4 to v1
M P₁ 0000 P3 Give the adjacency matrix M associated with the directed graph above. P5 ОРА Those longest possible walks all start at the vertex P1 for the vertex P₁, P2 for the vertex P₂, etc. P₂ The smallest integer value n for which M" = 0 (where 0 represents a zero matrix) is This indicates that the longest walk between any two vertices in the graph would have length and end at the vertex (based on the matrix M"-1). Write
Solve b (i and ii) only
2. Which of the following is a correct representation of 2v given the row matrix v = [1 2]? A. В. D. 14 2 4 • 2 4 3. Given the graph at the right, which of the following row matrices is being represented? В. [-1 3 2] A. [1 3 2] C. [1 2 3] D. [2 3 1] 4. What is the length of the row matrix u = [-2 42 А. 2 C. V20 D. 2V2 Al makes with the horizontal x- axis? В. 4

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Question 4 Let M be the following matrix of a directed graph 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1. Draw a diagram of directed graph. 2. Find a similar interpretation for the values of the non-diagonal enteries of MTM. 3. Compute MT M.