=5 nodes and L=Consider the directed network G = (V,E) with N8 links, in whichnode 1 points to nodes 2 and 3, node 2 points to node 4, node 3 points to nodes 2 and4, node 4 points to node 2, and node 5 points to nodes 3 and 4.(a) Draw the network and write down its adjacency matrix A.(b) How many weakly-connected components and how many non-trivial (i.e. withmore than one node) strongly-connected components are there in the network?List all the nodes belonging to each one of these components. List all the nodesbelonging, respectively, to the in-component and the out-component of each of thenon-trivial strongly-connected components.

(a) First, Draw the network according to the given information: The adjacency matrix A for this…

Answered: = 5 nodes and L = Consider the directed…

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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4. Membership in a Span: For every item: (i) apply the Modified Gauss-Jordan Algorithm to determine if b is in Span(S); (ii) write the solution vector i if there are solutions to the corresponding augmented matrix; (iii) express b as a linear combination of the vectors in S in the simplest possible way, and check directly that your answer is correct. b = (-4, 2,–3); S = {(7,4,–6), (–5,-2, 3)} а. b. b = (-4, 2,-4); S = {(7,4,–6), (-5,–2, 3)} b = (9, 7,-8, 2); S = {(5,-3, 2, 6), (-2,–3, 5, 8), (–5, 4,–2,–3)} d. b = (-10, 13,–4, 9); S = {(5,-3, 2, 6), (–5, 4,–2,–3), (-5, 7,–2, 6)} Б - (13, 14, -18, -11)}; S = {(5,-3, 2, 6), (-2,–3, 5, 8), (–5, 4,–2,–3), (11, 10,–13,–6)} b = (8,-9,-8, 15,–3), S = {(6,0,4, 3, 2), (3, 2, 7, 1,–2), (2, 1, 2, –1, 3)} Б - (-4,-1,4, 7, -9), S - {{3, 2, 7, 1, -2), (2, 1, 2, -1, 1), (1, 0, -3, -3, 4)} h. Б - (-3, 6, -1,-9, -4), S = {(6,0,–1, 3, 2), (3, 2,–3, 1,–2), (0,–4, 5, 1, 6), (3,–2, 1, 3, 3)} с. е. f. g.
3. Represent the following graph using 1) adjacency list 2) an an adjacency matrix. a e
Consider the adjacency matrix 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 of a graph with nodes labeled a,b,c,d,e and f and lexiographically ordered rows and columns. 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 0. Suppose the above adjacency matrix identifies the network in a small company, where nodes represent workers and edges indicate that those workers interact during the week. The company has a single team leader and two different projects, one larger than the other. Workers in the same project interact often during the week. a) State which node represents the team leader, justifying your answer. b) State whether all workers are involved in at least one project and whether there is any worker, apart from the team leader, who works simultaneously on both projects. c) Explain what happens to the graph if the team leader suddenly resigns. Your response should be written in sentences.
Consider the adjacency matrix 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 of a graph with nodes labeled a,b,c,d,e and f and lexiographically ordered rows and columns. 1 0 1 1 0 0 Lo 1 0 1 0 0 Suppose the above adjacency matrix identifies the network in a small company, where nodes represent workers and edges indicate that those workers interact during the week. The company has a single team leader and two different projects, one larger than the other. Workers in the same project interact often during the week. b) State whether all workers are involved in at least one project and whether there is any worker, apart from the team leader, who works simultaneously on both projects.
Help with number 4 please, a and b
1.28 Show that the nonzero rows of an echelon form matrix form a linearly indepen- dent set.
May you help me please :)!!
For a given network with 4 x 7 node-link incidence matrix, how many non-zero values will exist in the node-node adjacency matrix?
Consider the network with adjacency matrix A given by Is the network Select one or more: a. Weighted b. Unweighted C. Directed d. Simple 0 0 A = 1 0 1 0 1 0 0 0 0 0 0 0 101 0 1) 0 1 0 0 1 0
May you help me please :)!!

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