[1Let A =|1[212b)1 be the adjacency matrix for the graph G, with1vertices vi, V2, V3.i)Find the number of walks of length 2, from vị to vị.[2ii)Draw the graph G and label the edges e; (i = 1, 2, 3, ...)[2iii)Write down the walks of length 2 from vị to Vi. Whichones are simple circuits?[3[111011c)The matrix M =represents the relations R defined on1L1the set A ={1, 2, 3, 4}.i)List the ordered pairs in the relation R.[2ii)Draw the graph representing the relation R.d)How many edges does a 50-regular graph with 100 vertices have? [2

Answered: Image /qna-images/answer/92b579ed-a6d3-473b-89a8-a94655b49b4c.jpg

[1 1 21 b) Let A = |1 0 1 be the adjacency matrix for the graph G, wit l2 1 vertices vị, V2, V3. i) Find the number of walks of length 2, from vị to vị. ii) Draw the graph G and label the edges e; (i = 1, 2, 3, ...) iii) Write down the walks of length 2 from vi to Vi. Which ones are simple circuits?

[1 1 21 b) Let A = |1 0 1 be the adjacency matrix for the graph G, wit l2 1 vertices vị, V2, V3. i) Find the number of walks of length 2, from vị to vị. ii) Draw the graph G and label the edges e; (i = 1, 2, 3, ...) iii) Write down the walks of length 2 from vi to Vi. Which ones are simple circuits?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 79EQ

See similar textbooks

Similar questions

Show that the three points (x1,y1)(x2,y2) and (x3,y3) in the a plane are collinear if and only if the matrix [x1y11x2y21x3y31] has rank less than 3.
Which of the following are true for the adjacency matrix of the attached graph? 1. ||A||F = 4 2. A[1,.... ,1]T gives the vector of all out-degrees (number of edges out from a vertex) 3. ||A|| infiniti = 3 4. A is symmetric
Show that any isometry of R^n which fixes the origin is linear, and hence must be of the form f(x) = Ax for some orthogonal matrix A ∈ O(n).
The matrix A = " 1 0 0 2 # is a linear map from R 2 to R 2 . Draw the modified shape of the circle x 2 + y 2 = 1 after applying A on R 2
Draw the multigraph G whose adjacency matrix A is AG= 0 1 2 0 1 1 1 0 2 1 0 0 0 1 0 1
Consider the adjacency matrix for a graph that is shown below. Answer the following questions by examining the matrix and its powers only, not by drawing the graph. Show your work in a way that makes your reasoning clear. (a) How many walks of length 2 are there from v1 to v3? (b) How many walks of length 3 are there from v1 to v2?
Consider a linear transformation TT from R3R3 to R2R2 for which... Find the matrix AA of TT.
The following is an adjacency matrix for a graph: ? = [0 1 1 01 0 2 11 2 0 10 1 1 1]Answer the following questions by examining the matrix and its powers only, not bydrawing the graph:a) How many walks of length 2 are there from v2 to v3?b) How many walks of length 2 are there from v3 to v4?c) How many walks of length 3 are there from v1 to v4?d) How many walks of length 3 are there from v2 to v3?
Determine whether the linear transformation T is invertible by considering its matrix with respect to th e standard bases. If T is invertible, find T-1 . T: P2--->R2 defined by T(p(x)) ,B = {1, x, x2}, C = {e1, e2}, v = p(x) = a + bx + cx2
Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is, find a function t → z(t), a ≤ t ≤ b such that the range of the function is the set of all points of the said line segment
Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is a reflection over the line y=−4x.
Determine whether the linear transformation T is invertible by considering its matrix with respect to th e standard bases. If T is invertible, find T-1• T : P1--->P1 defined by T(a + bx) = b -ax, B= C= {1,x}, v = p(x) = 4 + 2x