Introductory Combinatorics
5th Edition
ISBN: 9780136020400
Author: Richard A. Brualdi
Publisher: Prentice Hall
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Question
Chapter 3, Problem 6E
To determine
To generalize: The results obtained in Exercise 4 and 5.
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Question 4 Find an equation of
(a) The plane through the point (2, 0, 1) and perpendicular to the line x =
y=2t, z=3+4t.
3t,
(b) The plane through the point (3, −2, 8) and parallel to the plane z = x+y.
(c) The plane that contains the line x =
parallel to the plane 5x + 2y + z = 1.
1+t, y2t, z = 43t and is
(d) The plane that passes through the point (1,2,3) and contains the line
x = 3t, y=1+t, and z = 2 – t.
(e) The plane that contains the lines L₁ : x = 1 + t, y = 1 − t, z =
=
L2 x 2s, y = s, z = 2.
2t and
2
5x
+
2–49
2
x+10x+21
Chapter 3 Solutions
Introductory Combinatorics
Ch. 3 - Prob. 1ECh. 3 - Prob. 2ECh. 3 - Prob. 3ECh. 3 - Prob. 4ECh. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - Prob. 7ECh. 3 - Use the pigeonhole principle to prove that the...Ch. 3 - Prob. 9ECh. 3 - A child watches TV at least one hour each day for...
Ch. 3 - A student has 37 days to prepare for an...Ch. 3 - Show by example that the conclusion of the Chinese...Ch. 3 - *Let S be a set of six points in the plane, with...Ch. 3 - Prob. 14ECh. 3 - Prove that, for any n + 1 integers a1, a2,…,an+1,...Ch. 3 - Prob. 16ECh. 3 - There are 100 people at a party. Each person has...Ch. 3 - Prove that of any five points chosen within a...Ch. 3 - Prove that of any five points chosen within an...Ch. 3 - Prove that r(3, 3, 3) ≤ 17.
Ch. 3 - Prove that r(3, 3, 3) ≥ 17 by exhibiting a...Ch. 3 - Prob. 22ECh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - A collection of subsets of {1, 2, …, n} has the...Ch. 3 - At a dance party there are 100 men and 20 women....Ch. 3 - Prob. 29E
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