13. Use the handshake theorem to find the number of edges of the graph with the followingadjaceny matrix.A(G) =1 1 11 1111 11 1 111 1111

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Answered: Use the handshake theorem to find the…

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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The matrix M represents a linear transformation of two-dimensional space and det(M) = 2. What can be said about the area of a region in the plane compared to the area that it is sent to under the transformation? The area of the region is one-half as large.The area of the region is one-third as large. The area of the region triples.The area of the region doubles. The linear transformation T sends all of three-dimensional space to a line. What can you say about the value of the determinant of the matrix representing the transformation? The determinant is negative.The determinant is 0. The absolute value of the determinant is less than 1.
(1) A directed graph G is defined with the following adjacency matrix. Label the nodes of G as 1,2,3, 4 and plot G. (1 0 0 1 0 100 0 010 1001, (2) Let f(x) = x* + (-2)x² + 3x + 4. Re-write f(x) in the telescoping form that can be used in Horner's method.
(b) Find the adjacency matrix for one of the following directed graphs: (i) V1 e3 e2 V3 02 (ii) V4 C V1 es e6 e4 e2 e3 02
A square matrix [A] is diagonally dominant if (A) la,l2Σa- 1, 2." (B) a, > Ea,i = 1, 2, ...,n and a, >E a, for any i 1, 2, .., n %3D (C) a,> Ea, = 1, 2 ....n and a,|>E, for any i = 1, 2, ..n (D) a,l2 Σa i=1, 2 " = 1, 2, ....n
). (a) Given the points (1,2), (2,6), and (4,1). Find the equation of the straight line that best fits these points. (b) Find P, the projection matrix on C(A), where A = (c) Verify that P² = P. 1 1 12 1 4
Solve A part only
Home work Q: Find the minimum poynomial for the following matrices. Is A diagonali zable -2 2 -3 1- A = 2 - A 2 -6 -1 -2 -2
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 .)
(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.
3. Let G be a siugle graph with vertices M,V2, Vs, V4 aud Vg. Let 0101 10I0I 01011 A - be ts adjacaney matrix. ( Find all paths of leugth 3 be tween Vq and V (b) V and Vu It B. amazon pe here to search
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.
A B D 10. (a) Show the graph above and its adjacency matrix. (b) Find the number of walks of length 4 that start at B and end at A or C. Explain your work.

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Use the handshake theorem to find the number of edges of the graph with the following adjaceny matrix. A(G) = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1