2. Provide the graph of the following incidence matrices.a)10 0 00 0 11010 101Lo 0 1 0 I1.b)- 1- 111-1- 1I 0 1-1

Answered: Image /qna-images/answer/8b8856b8-5e0f-4da7-abec-5f96437ec3b4.jpg

Answered: 2. Provide the graph of 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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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
3. In the configuration illustrated in Fig. 1 the camera matrices are P₁ = [10] and Pr = [I t], where I is the identity matrix and t = (-6, 0, 0). The point Q has coordinates (3, 0, 3)T. Assume b = 6 cm, f = 1 cm. Compute the image of Q in unit of cm on the image plane of the camera on the left and the corresponding epipolar line on the image plane of the camera on the right. Z X1 b A Fig. 1 P = (Xp, Yp, Zp) X
2. Consider the following distance matrix for an undirected graph and solve the 1-center problem (∞ means no edge exists). 2 4 Ce || |
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 .)
Determine the incidence matrix of the graph G. V3 e2 e3 V1 ei V2 e4 V4 e6 V6 V7 V5 ez es V8
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)
Let V = {V₁, V2, V3} and R = {(V₁, V₁), (V₁, V2), (V₁, V3), (V2, V2), (V2, V3), (V3, V₁)}. a. Draw a directed graph to represent R and find MR. b. Find So, S₁, S2, and the shortest path matrix, S3.
5. Diagonalize A (if possible), that is, find a representation of the form A = PDP-¹, where D is diagonal, for ₁ 0 1 1 +]; ; (d) A = 0 0 1 001 (c) A 11 0 00
Use powers of adjacency matrices to determine the number ofpaths of the specified length between the given vertices. length 2, v2 to v3
Rahul p.
3. Consider the matrix (in Matlab notation) A = [1, a; a, 1] where the value of a gets close to 1, i.e., a = 0.9; 0.99; 0.999, etc. Study how it maps the unit circle x, y = Ax.
consider matrix A provided in the image. a) Calculate A2.b) Calculate (3A)2 - At.

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2. Provide the graph of the following incidence matrices. a) 1 1 10 0 1 0 0 1 10 0 1010 1 0 1011 b) I -1 0 0 -1 -1 I 0 I O1