Explanation Given information: Let p 1 = [ 1 0 2 ] , p 2 = [ − 1 2 1 ] , n 1 = [ 1 1 − 2 ] , and n 2 = [ − 2 1 3 ] . Let H 1 be the hyperplane in R 3 through p 1 with normal vector n 1 . Let H 2 be the hyperplane through p 2 with normal vector n 2 . Calculation: Consider hyperplane as follows: H 1 = [ x : n 1 ⋅ x = d 1 ] (1) H 2 = [ x : n 2 ⋅ x = d 2 ] (2) Find the side of the points as shown below. d 1 = n 1 ⋅ p 1 Substitute [ 1 1 − 2 ] for n 1 and [ 1 0 2 ] for p 1 . d 1 = [ 1 1 − 2 ] ⋅ [ 1 0 2 ] = 1 − 4 = − 3 d 2 = n 2 ⋅ p 2 Substitute [ − 2 1 3 ] for n 2 and [ − 1 2 1 ] for p 2 . d 2 = [ − 2 1 3 ] ⋅ [ − 1 2 1 ] = 2 + 2 + 3 = 7 Solve the system as shown below. Substitute [ 1 1 − 2 ] for n 1 and − 3 for d 1 in Equation (1). [ 1 1 − 2 ] x = − 3 Substitute [ − 1 2 1 ] for n 2 and 7 for d 2 in Equation (2)

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Author: Lay

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Chapter 8.4, Problem 1PP

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An explicit description of H1∩H2 .

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Chapter 8.3, Problem 28E

Chapter 8.4, Problem 1E

Chapter 8 Solutions

EBK LINEAR ALGEBRA AND ITS APPLICATIONS

Ch. 8.1 - Plot the points v1=[10],v2=[12], v3=[31], and...Ch. 8.1 - In Exercises 14, write y as an affine combination...Ch. 8.1 - In Exercises 14, write y as an affine combination...Ch. 8.1 - In Exercises 14, write y as an affine combination...Ch. 8.1 - In Exercises 14, write y as an affine combination...Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E

Ch. 8.1 - Suppose that the solutions of an equation Ax = b...Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - In Exercises 11â€”20, mark each statement True or...Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Choose a set S of three points such that aff S is...Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.2 - Describe a fast way to determine when three points...Ch. 8.2 - Prob. 2PP Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - The conditions for affine dependence are stronger...Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Let T be a tetrahedron in standard position, with...Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - In Exercises 21-24, a, b, and c are noncollinear...Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.3 - Prob. 1PP Ch. 8.3 - Let S be the set of points on the curve y = 1/x...Ch. 8.3 - Prob. 1E Ch. 8.3 - Describe the convex hull of the set S of points...Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Repeat Exercise 9 for the points q1, , q5 whose...Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Let v1 = [10], v2 = [12], v3 = [42], v4 = [40],...Ch. 8.3 - In Exercises 17-20, prove the given statement...Ch. 8.3 - In Exercises 17-20, prove the given statement...Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.4 - Prob. 1PP Ch. 8.4 - Let L be the line in 2 through the points [14] and...Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - In Exercises 3 and 4, determine whether each set...Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - In Exercises 7-10, let H be the hyperplane through...Ch. 8.4 - Prob. 11E Ch. 8.4 - Let a1=[215], a2=[313], a3=[160], b1=[051],...Ch. 8.4 - Prob. 13E Ch. 8.4 - Let F1 and F2 be 4-dimensional flats in 6, and...Ch. 8.4 - In Exercises 15-20, write a formula for a linear...Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - In Exercises 15-20, write a formula for a linear...Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - In Exercises 21â€”28, mark each statement True or...Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prove that the convex hull of a bounded set is...Ch. 8.5 - Find the minimal representation of the polytope P...Ch. 8.5 - Given points p1 = [10], p2 = [23], and p3 = [12]...Ch. 8.5 - Given points p1 = [01], p2 = [21], and p3 = [12]...Ch. 8.5 - Repeat Exercise 1 where m is the minimum value of...Ch. 8.5 - Repeat Exercise 2 where m is the minimum value of...Ch. 8.5 - In Exercises 5-8, find the minimal representation...Ch. 8.5 - In Exercises 5-8, find the minimal representation...Ch. 8.5 - In Exercises 5-8, find the minimal representation...Ch. 8.5 - In Exercises 5-8, find the minimal representation...Ch. 8.5 - Let S = {(x, y) : x2 + (y 1)2 1} {(3, 0)}. Is...Ch. 8.5 - Find an example of a closed convex set S in 2 such...Ch. 8.5 - Find an example of a bounded convex set S in 2...Ch. 8.5 - a. Determine the number of k-faces of the...Ch. 8.5 - a. Determine the number of k-faces of the...Ch. 8.5 - Suppose v1, , vk are linearly independent vectors...Ch. 8.5 - A k-pyramid Pk is the convex hull of a (k ...Ch. 8.5 - Prob. 16E Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Prob. 20E Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E Ch. 8.5 - Prob. 23E Ch. 8.5 - Let v be an element of the convex set S. Prove...Ch. 8.5 - If c and S is a set, define cS = {cx : x S}....Ch. 8.5 - Prob. 26E Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.6 - A spline usually refers to a curve that passes...Ch. 8.6 - Prob. 2PP Ch. 8.6 - Prob. 1E Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Let x(t) and y(t) be Bzier curves from Exercise 5,...Ch. 8.6 - Prob. 8E Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E Ch. 8.6 - Prob. 16E Ch. 8.6 - Prob. 17E Ch. 8.6 - Prob. 18E Ch. 8.6 - Explain why a cubic Bzier curve is completely...Ch. 8.6 - TrueType fonts, created by Apple Computer and...Ch. 8.6 - Prob. 22E Ch. 8 - Prob. 1SE Ch. 8 - Prob. 2SE Ch. 8 - Prob. 3SE Ch. 8 - Prob. 4SE Ch. 8 - Prob. 8SE Ch. 8 - Prob. 9SE Ch. 8 - Prob. 10SE Ch. 8 - Prob. 11SE Ch. 8 - Prob. 12SE Ch. 8 - Prob. 13SE Ch. 8 - Prob. 14SE Ch. 8 - Prob. 15SE Ch. 8 - Prob. 16SE Ch. 8 - Prob. 17SE Ch. 8 - Prob. 18SE Ch. 8 - Prob. 19SE Ch. 8 - Prob. 20SE Ch. 8 - Prob. 21SE Ch. 8 - Prob. 22SE Ch. 8 - Prob. 23SE Ch. 8 - Prob. 24SE Ch. 8 - Prob. 25SE Ch. 8 - Prob. 26SE Ch. 8 - Prob. 27SE Ch. 8 - Prob. 28SE Ch. 8 - Prob. 29SE Ch. 8 - Prob. 31SE Ch. 8 - Prob. 32SE Ch. 8 - Prob. 33SE Ch. 8 - Prob. 34SE Ch. 8 - Prob. 35SE

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An explicit description of H 1 ∩ H 2 .

Solution Summary: The author explains how to determine an explicit description of H_1cap, and the hyperplane.

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Chapter 8 Solutions