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- Draw the multigraph G whose adjacency matrix is 0 1 2 0 1 1 1 1 A 2 1 0 0 \o 1 0 1/ Show that the maximum number of edges in a graph with n-vertices is *C21.) Create an m-file with the name exercise_2_first_name_last_name. 2.) Use linspace() to create an array of times, call it t, from 0 to 5 with 200 points. 3.) Plug the points in t into the following equations: y, (t) = -4.9t2 + 3t and y,(t) = -4.9t2 + 7t where t is in seconds and y is in meters. These equations represent the heights of two objects thrown directly upward with initial positions y = 0 and initial speeds 3" and 7. 4.) Create a figure showing two graphs with the plot command. Graph one equation as green circles and the other as blue dots. You'll want to add the hold on command before the plot commands. It’ll let you graph more than one set of data points. 5.) Add the following labels using xlabel and ylabel: time (s) and height (m). When we graph quantities with units, we include the units in parenthesis directly after the name of the quantity. The reader must know what units are being plotted since they represent real quantities. 6.) Add the following title: Heights vs.…Determine whether the set in P_2 is linearly independent. S={x^2 , +1, 2 - 1, 2}
- 2. Show that a subset X of a matroid is a hyperplane if and only if X is a maximal non-spanning set. 13 ) Find all matroids having a unioue basis.A k-dimensional hypercube on 2^k vertices is defined recursively. The base case, a 1- dimensional hypercube, is the line segment graph. Each higher dimensional hypercube is constructed by taking two copies of the previous hypercube and using edges to connect the corresponding vertices (these edges are shown in gray). Here are the first three hypercubes: 10: O-O 2D: 3D: a. Prove that every k-dimensional hypercube has a Hamiltonian circuit (use induction).2. A lattice point is a point with integer coordinates such as (3,1). In how many ways can we pick 3 lattice points such that the coordinates of each point are positive integers less than 5, and the three points form a nondegenerate triangle?
- i) Consider the set S = {−6, −3, 0, 3, 6}. Draw a graph G whose set of verti- ces be S and such that for i, j ∈ S, ij ∈ E(G) if ij are related to a rule that t'u you choose to apply to i and j. (ii) A graph G of order 12 has as a set of vertices c1, c2, . . . , c12 for the do- ce configurations of figure 1. A movement on said board corresponds to moving a coin to an unoccupied square using the following two rules: 1. the gold coin can move only horizontally or diagonally, 2. the silver coin can move only vertically or diagonally. Two vertices ci, cj, i̸ = j are adjacent if it is possible to move ci to cj in a single movement. a) What vertices are adjacent to c1 in G? b) Draw the subgraph induced by {c2, c6, c9, c11}Question and answer are given, please explain how part c of this problem is obtained.Explain how to complete this:



