
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Chapter 11.2, Problem 33E
To determine
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1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
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2) Given the following matrices A =
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0
1] an
and B =
0
1
-3
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find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
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Chapter 11 Solutions
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 11.1 - Prob. 1TFQCh. 11.1 - Prob. 2TFQCh. 11.1 - Prob. 3TFQCh. 11.1 - In a graph G with two odd vertices, 1 and 2 , the...Ch. 11.1 - If a graph G has six odd vertices, to solve the...Ch. 11.1 - Prob. 6TFQCh. 11.1 - Prob. 7TFQCh. 11.1 - In the weighted graph the Chinese Postman Problem...Ch. 11.1 - Prob. 9TFQCh. 11.1 - In the unweighted graph n, n odd, the Chinese...
Ch. 11.1 - Solve the Chinese Postman Problem for each of the...Ch. 11.1 - Prob. 2ECh. 11.1 - 3. [BB] Solve the Chinese Postman Problem for the...Ch. 11.1 - In a graph G with two odd vertices, 1 and 2 , the...Ch. 11.1 - Solve the Chinese Postman Problem for each of the...Ch. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Solve the Chinese Postman Problem for the weighted...Ch. 11.1 - Prob. 9ECh. 11.1 - Prob. 10ECh. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.2 - Prob. 1TFQCh. 11.2 - Prob. 2TFQCh. 11.2 - Prob. 3TFQCh. 11.2 - Prob. 4TFQCh. 11.2 - Prob. 5TFQCh. 11.2 - Prob. 6TFQCh. 11.2 - Prob. 7TFQCh. 11.2 - Prob. 8TFQCh. 11.2 - Prob. 9TFQCh. 11.2 - Prob. 10TFQCh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prove Theorem 11.2.4: A digraph is Eulerian if and...Ch. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - 13. Label the vertices of each pair of digraphs in...Ch. 11.2 - 14. Consider the digraphs , shown.
(a) Find the...Ch. 11.2 - The answers to exercises marked [BB] can be found...Ch. 11.2 - In each of the following cases, find a permutation...Ch. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - [BB] if a graph G is connected and some...Ch. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - [BB] Apply the original form of Dijkstras...Ch. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - [BB] The Bellman-Ford algorithm can be terminated...Ch. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.3 - Prob. 1TFQCh. 11.3 - Prob. 2TFQCh. 11.3 - Prob. 3TFQCh. 11.3 - Prob. 4TFQCh. 11.3 - Prob. 5TFQCh. 11.3 - Prob. 6TFQCh. 11.3 - Prob. 7TFQCh. 11.3 - Prob. 8TFQCh. 11.3 - Prob. 9TFQCh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.4 - Prob. 1TFQCh. 11.4 - Prob. 2TFQCh. 11.4 - Prob. 3TFQCh. 11.4 - Prob. 4TFQCh. 11.4 - Prob. 5TFQCh. 11.4 - Prob. 6TFQCh. 11.4 - Prob. 7TFQCh. 11.4 - Prob. 8TFQCh. 11.4 - Prob. 9TFQCh. 11.4 - Prob. 10TFQCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.5 - Prob. 1TFQCh. 11.5 - Prob. 2TFQCh. 11.5 - Prob. 3TFQCh. 11.5 - Prob. 4TFQCh. 11.5 - Prob. 5TFQCh. 11.5 - Prob. 6TFQCh. 11.5 - Prob. 7TFQCh. 11.5 - Prob. 8TFQCh. 11.5 - Prob. 9TFQCh. 11.5 - 10. In a type scheduling problem, a vertex that...Ch. 11.5 - Prob. 1ECh. 11.5 - [BB] The construction of a certain part in an...Ch. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Prob. 5ECh. 11.5 - 6.(a) Find two different orientations on the edges...Ch. 11.5 - Prob. 7ECh. 11.5 - 8. Repeat Exercise 7 if, in addition to all the...Ch. 11.5 - Repeat Exercise 7 if A takes 6 months to complete...Ch. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - 17. The computer systems manager in mathematics...Ch. 11 - Solve the Chinese Postman Problem for the two...Ch. 11 - Prob. 2RECh. 11 - 3. Solve the Chinese Postman Problem for the...Ch. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - 11. Let and assume that the complete graph has...Ch. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Use a version of Dijkstras algorithm to find a...Ch. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - 20. The following chart lists a number of tasks...Ch. 11 - Prob. 21RE
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