Introductory Combinatorics
Introductory Combinatorics
5th Edition
ISBN: 9780136020400
Author: Richard A. Brualdi
Publisher: Prentice Hall
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Chapter 11, Problem 20E
To determine

To prove: A graphs of order n with at least (n1)(n2)2+1 edges must be connected and find an example of a disconnected graph of order n with one fewer edge.

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Here is an augmented matrix for a system of equations (three equations and three variables). Let the variables used be x, y, and z: 1 2 4 6 0 1 -1 3 0 0 1 4 Note: that this matrix is already in row echelon form. Your goal is to use this row echelon form to revert back to the equations that this represents, and then to ultimately solve the system of equations by finding x, y and z. Input your answer as a coordinate point: (x,y,z) with no spaces.
1 3 -4 In the following matrix perform the operation 2R1 + R2 → R2. -2 -1 6 After you have completed this, what numeric value is in the a22 position?
5 -2 0 1 6 12 Let A = 6 7 -1 and B = 1/2 3 -14 -2 0 4 4 4 0 Compute -3A+2B and call the resulting matrix R. If rij represent the individual entries in the matrix R, what numeric value is in 131? Input your answer as a numeric value only.

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Introductory Combinatorics

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