Explanation Given information: The given points are, a. p 1 = [ 0 − 19 − 5 ] b. p 2 = [ 1.5 − 1.3 − 0.5 ] c. p 3 = [ 5 − 4 0 ] Let S = { b 1 , b 2 , b 3 } with b 1 = [ 2 1 1 ] , b 2 = [ 1 0 − 2 ] , and b 3 = [ 2 − 5 1 ] . Calculation: Write the points in the matrix form as [ b 1 b 2 b 3 p 1 p 2 p 3 ] . A = [ 2 1 2 0 1.5 5 1 0 − 5 − 19 − 1.3 − 4 1 − 2 1 − 5 − 0.5 0 ] Let R1, R2, and R3 be the row 1, row 2, and row 3 of the matrix respectively. Perform the row reduction of the matrix as follows: Replace R1 by R1 → R1 ( 1 2 ) . A = [ ( 1 2 ) 2 ( 1 2 ) 1 ( 1 2 ) 2 ( 1 2 ) 0 ( 1 2 ) 1.5 ( 1 2 ) 5 1 0 − 5 − 19 − 1.3 − 4 1 − 2 1 − 5 − 0.5 0 ] R1 → R1 ( 1 2 ) = [ 1 1 2 1 0 3 4 5 2 1 0 − 5 − 19 − 13 10 − 4 1 − 2 1 − 5 − 5 10 0 ] Replace R2 by R2 → ( − 1 ) R1+R2 . A = [ 1 1 2 1 0 3 4 5 2 − 1 + 1 ( − 1 2 ) − 1 + ( − 5 ) 0 − 19 { ( − 1 ) 3 4 + − 13 10 } ( − 1 ) 5 2 − 4 1 − 2 1 − 5 − 5 10 0 ] R2 → ( − 1 ) R1+R2 = [ 1 1 2 1 0 3 4 5 2 0 − 1 2 − 6 − 19 − 41 20 − 13 2 1 − 2 1 − 5 − 5 10 0 ] Replace R3 by R3 → ( − 1 ) R1+R3 . = [ 1 1 2 1 0 3 4 5 2 0 − 1 2 − 6 − 19 − 41 20 − 13 2 − 1 + 1 − 1 2 − 2 − 1 + 1 0 − 5 ( − 1 ) ( 3 4 ) + − 5 10 0 ] R3 → ( − 1 ) R1+R3 = [ 1 1 2 1 0 3 4 5 2 0 − 1 2 − 6 − 19 − 41 20 − 13 2 0 − 5 2 0 − 5 − 5 4 − 5 2 ] Replace R2 by R2 → R2 ( − 2 ) . = [ 1 1 2 1 0 3 4 5 2 ( − 2 ) 0 ( − 2 ) − 1 2 ( − 2 ) − 6 ( − 2 ) − 19 ( − 2 ) − 41 20 ( − 2 ) − 13 2 0 − 5 2 0 − 5 − 5 4 − 5 2 ] R2 → R2 ( − 2 ) = [ 1 1 2 1 0 3 4 5 2 0 1 12 38 41 10 13 0 − 5 2 0 − 5 − 5 4 − 5 2 ] Replace R3 by R3 → R2 ( 5 2 ) + R3

Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e

5th Edition

ISBN: 9781323132098

Author: Thomas, Lay

Publisher: PEARSON C

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Chapter 8.3, Problem 4E

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To find: Which one among p1, p2, and p3 are in Conv S.

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Chapter 8.3, Problem 3E

Chapter 8.3, Problem 5E

Chapter 8 Solutions

Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e

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 - a. If S = {x}, then aff S is the empty set. b. A...Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Choose a set S of three points such that aff S is...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 - Prob. 25E Ch. 8.1 - Prob. 26E 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 - In Exercises 9 and 10, mark each statement True or...Ch. 8.2 - a. If{v1,....,vp} is an affinely dependent set in...Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - The conditions for affine dependence are stronger...Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Let T be a tetrahedron in standard position, with...Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - In Exercises 21-24, a, b, and c are noncollinear...Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E 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. 6E 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 - In Exercises 11 and 12, mark each statement True...Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Let v1 = [10], v2 = [12], v3 = [42], v4 = [40],...Ch. 8.3 - Prob. 16E 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. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E 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 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Let p=[41], Find a hyperplane [f : d] that...Ch. 8.4 - Let q=[23] and p=[61]. Find a hyperplane [f : d]...Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E 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 - In Exercises 16 and 17, mark each statement True...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 - Find an example to show that the convexity of S is...Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E 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 - In Exercises 11 and 12, mark each statement True...Ch. 8.6 - In Exercises 11 and 12, mark each statement True...Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E 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. 18E

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Which one among p 1 , p 2 , and p 3 are in Conv S .

Solution Summary: The author explains that p_2 is in Conv S.

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Chapter 8 Solutions