3. Draw the directed graph that represents for R = {(a, a), (a, b), (b, c), (c, c), (c, a)(c, b), (d, c), (d, a)}

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Answered: 3. Draw the directed graph that…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 4CM: Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4,...

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Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)
4. Let G = (V, E) be a graph with vertex-set V = {1, 2, 3, 4, 5, 6} and edge-set E = {(1, 2), (3, 2), (3, 4), (5, 4), (5, 6), (1, 6), (1, 3), (6,4)}. (a) Draw the graph. Find (b) maximal degree, i.e. A(G), (c) minimal degree, i.e. 8(G), (d) the size of biggest clique, i.e. w(G), (e) the size of biggest independent set, i.e. a(G), ter (f) the minimal number of colours needed to color the graph, i.e. x(G).
5. Draw a directed graph for the relation with coordinate pairs (a, b), (a, d), (b, b), (b, d), (c, a), (c, b) and (d, b).
Consider the graph G with • V(G) = {2,3,6} • e(G) = {a, b, c, d, e, f, g} •E(G) = {(a, [2,2]), (b, [3,3]), (c, [6,6]), (d, [2,6]), (e, [6,2]), (f, [3,6]), (g, [6,3])} Using edge connectivity, we can define the relation R = {(2, 2), (3, 3), (6, 6), (2, 6), (6, 2), (3, 6), (6,3)} Which of the following statements are true? [More than one statement may be true.] R is reflexive. R is symmetric. R is transitive. R is antisymmetric.
Compute the vertex set V and edge set E of the graph G = (V,E) whose Prufer Code is (3, 3, 3,3, 3, 3). Select one: OV={1,2,...,8} and E = {(1,3), (2, 4), (4, 3), (5, 3), (6, 3), (7, 3), (8, 7)} {(1,4), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 3)} %3D OV={1,2,..., 8} and E = OV= {1,2,... ,8} and E = {(1, 4), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 7)} OV= {1,2,..., 8} and E = {(1,3), (2, 3), (4, 3), (5, 3), (6, 3), (7, 3), (8, 3)} Clear my choice
The figure below shows a directed graph G: 1 3 2 4 Which edge is not in G 3. а. (1, 3) b. (2, 3) с. (3, 4) d. (4, 3)
1. Draw the graph G = (V, E) with vertex set V = {a, b, c, d, e, f, g, h} and edge set{(a, b), (a, e), (b, c), (b, d), (c, d), (c, g), (d, e)(e, ƒ), (f, g), (f, h), (g, h)}. a) Draw G – (d, e). b) Draw the subgraph of G induced by {c, d, e, f}.
For the directed graphs, draw the graph and show: A, A2 , A3, A4, A* , where A is the adjacency matrix for the edge set as a relation. (a) G1 = [{1, 2, 3, 4}]; (b) G2 = [{1, 2, 3, 4}]; Hint: Long matrix multiplications are not required, think about what for each of the matrices it means for a cell to contain a value of 1.
Construct a simple graph with vertices V, W, X, Y whose degrees are 1, 2, 0, 1 What is the edge set?
The value y (in 1982–1984 dollars) of each dollar paid by consumers in each of the years from 1994 through 2008 in a country is represented by the ordered pairs. (1994, 0.677) (1995, 0.655) (1996, 0.639) (1997, 0.618) (1998, 0.609) (1999, 0.605) (2000, 0.580) (2001, 0.565) (2002, 0.557) (2003, 0.542) (2004, 0.531) (2005, 0.516) (2006, 0.499) (2007, 0.478) (2008, 0.461) (a) Use a spreadsheet software program to generate a scatter plot of the data. Let t = 4 represent 1994. Do the data appear linear? Yes or No (b) Use the regression feature of the spreadsheet software program to find a linear model for the data. (Let t represent time. Round your numerical values to four decimal places.) y = (c) Use the model to predict the value (in 1982–1984 dollars) of 1 dollar paid by consumers in 2010 and in 2013. (Round your answers to two decimal places.) 2010 $ 2013 $ Discuss the…
An artist creates the basic pattern for a tablecloth by creating two similar triangles, AABC and AABC , in the coordinate plane. • The vertices of AABC are A(1, 2) , B(1, 3), and C(3, 2). • The vertices of AA BC' are A (3, - 6), B (3, - 9) , and C' (9, – Which of these could be a sequence of two transformations that maps AABC to AABC ? Choose all that are correct. Dilation by a factor of 3 about the origin, followed by reflection across the a -axis. A. B. Reflection across the I -axis, followed by dilation by a factor of 3 about the origin. C. Dilation by a factor of 3 about the origin, followed by reflection across the y -axis. D. Reflection across the y -axis, followed by dilation by a factor of 3 about the origin. Dilation by a factor of -3 about the origin, followed by reflection across the y -axis. E. F. Reflection across the z -axis, followed by dilation by a factor of -3 about the origin.
36 Consider a directed graph where V = {a, b, c, d) and E = {(a,b), (b.c), (c,d). (a.c), (d.b)}. How many 3-cycles are in G=(VE) ? 00 01 03 2

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3. Draw the directed graph that represents for R = {(a, a), (a, b), (b, c), (c, c), (c, a) (c, b), (d, c), (d, a)}