To prove: A is the adjacency matrix of a tournament with n players if and only A + A T = J − I , where I is the n × n identity matrix and J is the n × n matrix consisting entirely of 1’s.

Question

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Answer 1

Question

Chapter 11.4, Problem 3E

(a)

To determine

To prove: A is the adjacency matrix of a tournament with n players if and only A+AT=J−I, where I is the n×n identity matrix and J is the n×n matrix consisting entirely of 1’s.

(b)

To determine

The transpose. If A is the adjacency matrix of a tournament.

(c)

To determine

The reason that Let P be an n×n permutation matrix, that is, a matrix obtained from the n×n identity matrix by rearranging its rows. If A is the adjacency matrix of a tournament, so is PAPT.

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Answer 2

Question

Chapter 11.4, Problem 3E

(a)

To determine

To prove: A is the adjacency matrix of a tournament with n players if and only A+AT=J−I, where I is the n×n identity matrix and J is the n×n matrix consisting entirely of 1’s.

(b)

To determine

The transpose. If A is the adjacency matrix of a tournament.

(c)

To determine

The reason that Let P be an n×n permutation matrix, that is, a matrix obtained from the n×n identity matrix by rearranging its rows. If A is the adjacency matrix of a tournament, so is PAPT.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 11.4, Problem 3E

(a)

To determine

To prove: A is the adjacency matrix of a tournament with n players if and only A+AT=J−I, where I is the n×n identity matrix and J is the n×n matrix consisting entirely of 1’s.

(b)

To determine

The transpose. If A is the adjacency matrix of a tournament.

(c)

To determine

The reason that Let P be an n×n permutation matrix, that is, a matrix obtained from the n×n identity matrix by rearranging its rows. If A is the adjacency matrix of a tournament, so is PAPT.

Expert Solution & Answer

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Answer 4

Question

Chapter 11.4, Problem 3E

(a)

To determine

To prove: A is the adjacency matrix of a tournament with n players if and only A+AT=J−I, where I is the n×n identity matrix and J is the n×n matrix consisting entirely of 1’s.

(b)

To determine

The transpose. If A is the adjacency matrix of a tournament.

(c)

To determine

The reason that Let P be an n×n permutation matrix, that is, a matrix obtained from the n×n identity matrix by rearranging its rows. If A is the adjacency matrix of a tournament, so is PAPT.

Expert Solution & Answer

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Answer 5

Chapter 11.4, Problem 3E

(a)

To determine

To prove: A is the adjacency matrix of a tournament with n players if and only A+AT=J−I, where I is the n×n identity matrix and J is the n×n matrix consisting entirely of 1’s.

(b)

To determine

The transpose. If A is the adjacency matrix of a tournament.

(c)

To determine

The reason that Let P be an n×n permutation matrix, that is, a matrix obtained from the n×n identity matrix by rearranging its rows. If A is the adjacency matrix of a tournament, so is PAPT.

Answer 6

Chapter 11.4, Problem 3E

(a)

To determine

To prove: A is the adjacency matrix of a tournament with n players if and only A+AT=J−I, where I is the n×n identity matrix and J is the n×n matrix consisting entirely of 1’s.

Answer 7

Chapter 11.4, Problem 3E

(a)

To determine

To prove: A is the adjacency matrix of a tournament with n players if and only A+AT=J−I, where I is the n×n identity matrix and J is the n×n matrix consisting entirely of 1’s.

Answer 8

(b)

To determine

The transpose. If A is the adjacency matrix of a tournament.

Answer 9

(b)

To determine

The transpose. If A is the adjacency matrix of a tournament.

Answer 10

(c)

To determine

The reason that Let P be an n×n permutation matrix, that is, a matrix obtained from the n×n identity matrix by rearranging its rows. If A is the adjacency matrix of a tournament, so is PAPT.

Answer 11

(c)

To determine

The reason that Let P be an n×n permutation matrix, that is, a matrix obtained from the n×n identity matrix by rearranging its rows. If A is the adjacency matrix of a tournament, so is PAPT.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 11.1 - Prob. 1TFQ Ch. 11.1 - Prob. 2TFQ Ch. 11.1 - Prob. 3TFQ Ch. 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. 6TFQ Ch. 11.1 - Prob. 7TFQ Ch. 11.1 - In the weighted graph the Chinese Postman Problem...Ch. 11.1 - Prob. 9TFQ Ch. 11.1 - In the unweighted graph n, n odd, the Chinese...

To prove: A is the adjacency matrix of a tournament with n players if and only A + A T = J − I , where I is the n × n identity matrix and J is the n × n matrix consisting entirely of 1’s.

Solution Summary: The author proves that A is the adjacency matrix of a tournament with n players if and only A+AT=J-I.

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To prove: A is the adjacency matrix of a tournament with n players if and only A+AT=J−I, where I is the n×n identity matrix and J is the n×n matrix consisting entirely of 1’s.

The transpose. If A is the adjacency matrix of a tournament.

The reason that Let P be an n×n permutation matrix, that is, a matrix obtained from the n×n identity matrix by rearranging its rows. If A is the adjacency matrix of a tournament, so is PAPT.

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