Question 23Consider the undirected graphs represented by the following adjacency matrices. Which statement is true?01100 1100 0 10 10 1 070 0 1 0 0 10110000 0010 0 1 1 0 1 1 1Θ 0 010 0101 1 0 1 0 10 11 0 0 0 1 0 1 00 0 0M1=0 1 1 0 1 10 1M2=1 0 0 1 0 1 1 10 0 10 1 0 0 0 000M3=%3D0 0 10 @ 1 0 0 0 1 0100Θ00 0 10 1 1 1 1 0 1 01 1 0 0 1 10 10 1 1 1 10 1 010 0 00 0 00 1 1 0 1 00 0T0 0 01 0 00 1 1 1 1 1 1 01 0 000 0Neither M2 nor M3 has an Euler path.Neither M1 nor M2 has an Euler path.The undirected graph represented by M2 contains an Euler circuit.The undirected graph represented by M3 contains an Euler circuit.The undirected graph represented by M1 contains an Euler circuit.

Given- Consider the undirected graphs represented by the following adjacency matrices. To find-…

Answered: Consider the undirected graphs…

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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Consider A to be the adjacency matrix for G 0 1 1 2 0 0 1 1000 1 100 1 1 2 0100 0 1 1 00 A = Then the size of the graph G is O 2 O 7 O None of the above O 3
Which of the following matrices are inverses of each other (select only one)? O O O | -30 5 4 6 3 -5 4 1 -2 7 -8 1 -2 3 2 4 1 0 1 0 -6 1 1 -9 -3 3 -1 2 3 -2 4 -1 0 3 0 0 3 30 1 0 -1 0 -12 1 0 0 1 1 1 0 1 -1 0 3 0 0 1 2 -5 3 -3 2 -1 3 1 3 [ 1 -3 2 -1 .]| 0 1 3-2 0 -5 5 0 7 -3 -3 1 0 0 1 3 -24 1 -1 0 1 0 0 2 -4 1 0 3 1 4 -30 -6 5 1 0 1 1 0 5 1 4 1 0 -30 -6 1 1 0 -12 -4 1 -8 1 -7 -9 10 -12 -15 17 1 1
Which matrix represents the number of walks of length 2 and how many walks of length 2 are in the graph G? b d a e G No answer provided [3 3 2 1 3] 2 4 3 2 3 2 33 2 3 3 3 2 а. [3 3 1 34, number of walks of length 2 is 61. [3 2 1 31 3 2 2 1 2 3 b. L3 3 3 2 1 31, number of walks of length 2 is 57. 2 2 1 21 [3 2 4 1 2 2 2 3 c. L3 2 2 1 3 2 3 1 31, number of walks of length 2 is 56. 2 [3 2 37 4 2 1 2 1 3 2 2 34, number of walks of length 2 is 58. H 2 3 31 N 33 32 N32 32 m N 12 3
Question 13given the adjacency matrices construct the corresponding graphs
Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 x 5 matrix A is the adjacency matrix for G. The matrices A² and A³ are given below. 0 1 0 0 0 0 0 10 0 10 0 0 0 10 0 1 0 0 1 1 0 1 10 0 0 0 010 0 0 0 0 10 0 0 1 1 0 1 10 1 0 Use the information given to answer the questions about the graph G. (a) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A* A² - A² .)
Question 13 A directed graph G has 5 vertices, numbered 1 through 5. The 5 x 5 matrix A is the adjacency matrix for G. The matrices A2 and A3 are given below. 00100 0 0 0 1 0 0 0 0 1 0 10 0 0 0 0 1 A20000 1 A³ = 1 0 1 0 0 10 10 0 01 0 1 0 0 0 1 0 1 00101 Which edge is not in the transitive closure of G? (2,4) ○ (5,5) ○ (1, 3) ○ (4,5)
4
-2 0 What is the transpose of matrix 2 3 -1 -2 0 2 3 a. 3 0. -1 1 b. 0 1 -2 2 3 3 c. 1 0 -1 -2 2 5 0 3 d. 0 1 -2 3 5. 1 0 3 2 Jump to... Follow Us f in 107
Select all of the following matrices that are diagonal matrices. 1 -1 -3 [3 0 0 4 2 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0
Drag each of the six matrices to the column above which the polynomial corresponds to its characteristic polynomial. 2 1 1 0 0 -4 5 0 1 4 2 2 -5 -6 -5 7 5 8 -x³ +5x² - 2x - 8 9 6 -13 -10 8 6 9 4 7 -7 16 -24 -3 4 0 (AD CAD CD 5 4 5 4 -3 8 9 8 -10 -4 -8 4 -8 13 0 0 -3 -r³+3x²+ 13x - 15 0 -³x² + 10x - 8 C Reset
QUESTION 14 The following matrix is the adjacency matrix corresponding to a directed graph. Determine if the following statements are true or false. If true, type T; if false, type F. A B C D E А ГО 1 1 0 0 B 1 0 0 1 0 C 0 0011 D E 0 0 0 0 1 0 1 0 0 0 a. Vertex A is reachable from vertex B. b. Vertex C is reachable from vertex B. c. Vertex B is reachable from vertex C. d. Vertex C is not reachable from vertex D.
Given two linear maps L, and L, such that their associated matrices are A,= and A,=1 -1 respectively. Find the matrix associated with the 2 2 3 -2 0 4 composite of linear maps L,oL, ? a. 6 2 3 3 0 4 b. 6 2 3 3 0 - 4 c. 6 -2 3 -3 0 -4 d. 6 -2 3 -3 0 4

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