EBK LINEAR ALGEBRA AND ITS APPLICATIONS
6th Edition
ISBN: 9780135851043
Author: Lay
Publisher: PEARSON CO
expand_more
expand_more
format_list_bulleted
Question
Chapter 7.3, Problem 14E
a)
To determine
To find:
The maximum value of
b)
To determine
To find:
A unit
c)
To determine
To find:
The maximum of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Find the maximum value of
Q(x) = –3x} + 5x} – 2x1x2,
||
subject to the constraint
구 + xg %=D1.
(Do not go on to find a vector where the maximum is attained.)
тах 2х, + Зх2 — Хз
s.t
X1 + 2x, + x3 = 5 (1)
-X1 + x2 + x3 >1 (2)
X1 + x2 + 2x3 <8 (3)
X1 2 0
(4)
X2 2 0
(5)
a. Which constraints are active at the point (2, 0, 3)?
b. Is the direction d=(-1, 1, -1) a feasible direction at (2, 0, 3)?
c. Is the direction d=(-1, 1, -1) an improving direction at (2, 0, 3)?
d. Could the point (2, 0, 3) be an optimal solution to the linear program?
e. Is the point (2, 0, 3) a basic solution? Justify your answer.
f. Is the point (2, 0, 3) an extreme point? Justify your answer.
g. Is the point (2, 0, 3) degenerate?
Find the maximum value of
Q(x) = 7x} + 3x – 2x1x2,
subject to the constraint
xỉ + x = 1.
(Do not go on to find a vector where the maximum is attained.)
Chapter 7 Solutions
EBK LINEAR ALGEBRA AND ITS APPLICATIONS
Ch. 7.1 - Show that if A is a symmetric matrix, then A2 is...Ch. 7.1 - Show that if A is orthogonally diagonalizable,...Ch. 7.1 - Determine which of the matrices in Exercises 1-6...Ch. 7.1 - Determine which of the matrices in Exercises 1-6...Ch. 7.1 - Determine which of the matrices in Exercises 1-6...Ch. 7.1 - Determine which of the matrices in Exercises 1-6...Ch. 7.1 - Determine which of the matrices in Exercises 1-6...Ch. 7.1 - Determine which of the matrices in Exercises 1-6...Ch. 7.1 - Determine which of the matrices in Exercises 7-12...Ch. 7.1 - Determine which of the matrices in Exercises 7-12...
Ch. 7.1 - Determine which of the matrices in Exercises 7-12...Ch. 7.1 - Determine which of the matrices in Exercises 7-12...Ch. 7.1 - Determine which of the matrices in Exercises 7-12...Ch. 7.1 - Determine which of the matrices in Exercises 7-12...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Orthogonally diagonalize the matrices in Exercises...Ch. 7.1 - Prob. 22ECh. 7.1 - Let A=[411141114]andv=[111]. Verify that 5 is an...Ch. 7.1 - Let A=[211121112],v1=[101],andv2=[111]. Verify...Ch. 7.1 - Prob. 25ECh. 7.1 - In Exercises 25—32, mark each statement True or...Ch. 7.1 - In Exercises 25—32, mark each statement True or...Ch. 7.1 - In Exercises 25—32, mark each statement True or...Ch. 7.1 - In Exercises 25—32, mark each statement True or...Ch. 7.1 - Prob. 30ECh. 7.1 - In Exercises 25—32, mark each statement True or...Ch. 7.1 - In Exercises 25—32, mark each statement True or...Ch. 7.1 - Show that if A is an n n symmetric matrix, then...Ch. 7.1 - Suppose A is a symmetric n n matrix and B is any...Ch. 7.1 - Suppose A is invertible and orthogonally...Ch. 7.1 - Suppose A and B are both orthogonally...Ch. 7.1 - Let A = PDP1, where P is orthogonal and D is...Ch. 7.1 - Suppose A = PRP1, where P is orthogonal and R is...Ch. 7.1 - Construct a spectral decomposition of A from...Ch. 7.1 - Construct a spectral decomposition of A from...Ch. 7.1 - Prob. 41ECh. 7.1 - Let B be an n n symmetric matrix such that B2 =...Ch. 7.1 - Prob. 43ECh. 7.2 - Describe a positive semidefinite matrix A in terms...Ch. 7.2 - Compute the quadratic form XTAX, when A=[51/31/31]...Ch. 7.2 - Prob. 2ECh. 7.2 - Find the matrix of the quadratic form. Assume x is...Ch. 7.2 - Find the matrix of the quadratic form. Assume x is...Ch. 7.2 - Find the matrix of the quadratic form. Assume x is...Ch. 7.2 - Find the matrix of the quadratic form. Assume x is...Ch. 7.2 - Make a change of variable, x = Py, that transforms...Ch. 7.2 - Let A be the matrix of the quadratic form...Ch. 7.2 - Classify the quadratic forms in Exercises 9-18....Ch. 7.2 - Classify the quadratic forms in Exercises 9-18....Ch. 7.2 - Classify the quadratic forms in Exercises 9-18....Ch. 7.2 - Classify the quadratic forms in Exercises 9-18....Ch. 7.2 - Classify the quadratic forms in Exercises 9-18....Ch. 7.2 - Classify the quadratic forms in Exercises 9-18....Ch. 7.2 - Prob. 17ECh. 7.2 - What is the largest possible value of the...Ch. 7.2 - What is the largest value of the quadratic form...Ch. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Exercises 23 and 24 show how to classify a...Ch. 7.2 - Exercises 23 and 24 show how to classify a...Ch. 7.2 - Show that if B is m n, then BTB is positive...Ch. 7.2 - Prob. 34ECh. 7.2 - Let A and B be symmetric n n matrices whose...Ch. 7.2 - Let A be an n n invertible symmetric matrix. Show...Ch. 7.3 - Let Q(x)=3x12+3x22+2x1x2. Find a change of...Ch. 7.3 - Prob. 2PPCh. 7.3 - In Exercises 1 and 2, find the change of variable...Ch. 7.3 - In Exercises 1 and 2, find the change of variable...Ch. 7.3 - In Exercises 3-6, find (a) the maximum value of...Ch. 7.3 - In Exercises 3-6, find (a) the maximum value of...Ch. 7.3 - In Exercises 3-6, find (a) the maximum value of...Ch. 7.3 - In Exercises 3-6, find (a) the maximum value of...Ch. 7.3 - Let Q(x)=2x12x22+4x1x2+4x2x3. Find a unit vector x...Ch. 7.3 - Let Q(x)=7x12+x22+7x324x1x24x1x3. Find a unit...Ch. 7.3 - Find the maximum value of Q(x)=7x12+3x222x1x2,...Ch. 7.3 - Find the maximum value of Q(x)=3x12+5x222x1x2,...Ch. 7.3 - Suppose x is a unit eigenvector of a matrix A...Ch. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - In Exercises 3-6, find (a) the maximum value of...Ch. 7.4 - Given a singular value decomposition, A = UVT,...Ch. 7.4 - Prob. 2PPCh. 7.4 - Find the singular values of the matrices in...Ch. 7.4 - Find the singular values of the matrices in...Ch. 7.4 - Find the singular values of the matrices in...Ch. 7.4 - Find the singular values of the matrices in...Ch. 7.4 - Find an SVD of each matrix in Exercises 512....Ch. 7.4 - Find an SVD of each matrix in Exercises 512....Ch. 7.4 - Find an SVD of each matrix in Exercises 512....Ch. 7.4 - Find an SVD of each matrix in Exercises 512....Ch. 7.4 - Find an SVD of each matrix in Exercises 512....Ch. 7.4 - Find an SVD of each matrix in Exercises 512....Ch. 7.4 - Find an SVD of each matrix in Exercises 512....Ch. 7.4 - Find an SVD of each matrix in Exercises 512....Ch. 7.4 - Find the SVD of A=[322232] [Hint: Work with AT.]Ch. 7.4 - In Exercise 7, find a unit vector x at which Ax...Ch. 7.4 - Suppose the factorization below is an SVD of a...Ch. 7.4 - Prob. 16ECh. 7.4 - In Exercises 1724, A is an m n matrix with a...Ch. 7.4 - In Exercises 1724, A is an m n matrix with a...Ch. 7.4 - In Exercises 1724, A is an m n matrix with a...Ch. 7.4 - In Exercises 1724, A is an m n matrix with a...Ch. 7.4 - Prob. 21ECh. 7.4 - In Exercises 1724, A is an m n matrix with a...Ch. 7.4 - Prob. 23ECh. 7.4 - In Exercises 1724, A is an m n matrix with a...Ch. 7.4 - Prob. 25ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.5 - The following table lists the weights and heights...Ch. 7.5 - The following table lists the weights and heights...Ch. 7.5 - In Exercises 1 and 2, convert the matrix of...Ch. 7.5 - In Exercises 1 and 2, convert the matrix of...Ch. 7.5 - Find the principal components of toe data for...Ch. 7.5 - Find the principal components of the data for...Ch. 7.5 - [M] A Landsat image with three spectral components...Ch. 7.5 - [M] The covariance matrix below was obtained from...Ch. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Suppose three tests are administered to a random...Ch. 7.5 - [M] Repeal Exercise 9 with S=[5424114245]. 9....Ch. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - The sample covariance matrix is a generalization...Ch. 7 - Prob. 1SECh. 7 - Prob. 2SECh. 7 - Prob. 3SECh. 7 - Prob. 4SECh. 7 - Mark each statement True or False. Justify each...Ch. 7 - Prob. 6SECh. 7 - Prob. 7SECh. 7 - Prob. 8SECh. 7 - Prob. 9SECh. 7 - Prob. 10SECh. 7 - Prob. 11SECh. 7 - Prob. 12SECh. 7 - Prob. 13SECh. 7 - Prob. 14SECh. 7 - Prob. 15SECh. 7 - Prob. 16SECh. 7 - Prob. 17SECh. 7 - Prob. 18SECh. 7 - Let A be an n n symmetric matrix of rank r....Ch. 7 - Let A be an n n symmetric matrix. a. Show that...Ch. 7 - Prob. 21SECh. 7 - Prob. 22SECh. 7 - Prob. 23SECh. 7 - Prob. 24SECh. 7 - If A is m n, then the matrix G = ATA is called...Ch. 7 - If A is m n, then the matrix G = ATA is called...Ch. 7 - Prove that any n n matrix A admits a polar...Ch. 7 - Prob. 28SECh. 7 - Prob. 30SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- 5. i ' Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 = 0 X2 + 4x3 – 3x4 = 0 X1arrow_forwardA certain country uses a progressive tax system. The amount of tax consists of a linear part proportional to the income and a nonlinear part depending on the income by a power law. The total amount of tax is determined by the formula T(W)=aW+(bW+c)p, where W is the income; p is the exponent, a,b,c are some positive numbers. At what level of income the tax rate will be minimal?arrow_forwardLet a, b, and x denote vectors in R,,. (a) Simplify 3a + (5b -2a) + 2(b - a). (b) If 5x - a = 2(a + 2x),solve for x in terms of a.arrow_forward
- 1 (a) Is the vector| 2 in the span of -1 and 2 ? Justify your answer 3 3 2 2 (b) Is the set linearly independent or linearly dependent? Justify your answer.arrow_forwardFind a general set of solution vectors x₂ = - 5x2 X₂ = x₁ + 3x₂arrow_forwardDetermine which vectors are solutions to a linear system: 2 x1 – 4x2 - x3 = 1 X1- 3x2+ X3 = 1 | 3x1 -5x2 - 3x3 = 1 Hint: linear system can have multiple solutions, this problem has multiple correct answers O (3,1,1) O (3, – 1,1) O (13,5,2) (블들리 13 5 -,2) 2 '2 O (17,7,5)arrow_forward
- Suppose the solution set of a certain system of linear equations can be described as to describe this set as a line in R³. Geometrically, the solution set is a line through (5, -6,0) parallel to (3,-8,1) wrong =5+3X3, X₂ = − 6-8x3, with x3 free. Use vectorsarrow_forwardFind the orthogonal trajectories of a system of confocal and coaxial parabolasarrow_forwardDetermine whether a=(2,-2,4), b=(3,5,4) and c=(0,1,1) are linearly dependent or not?arrow_forward
- 8.) Find a vector x such that 5x-2v=2(u-5x) SOLUTIONarrow_forwardSuppose y1 ( x), y2 ( x), y3 ( x) are three different functions of x. The vector space they span could have dimension 1, 2, or 3. Give an example of y1, y2, y3 to show each possibility.arrow_forwardSuppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the equation r1(t)=r2(t) may not produce all the points where the graphs of these functions intersect. Please Provide Unique Answer. Thank you!arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Matrix Factorization - Numberphile; Author: Numberphile;https://www.youtube.com/watch?v=wTUSz-HSaBg;License: Standard YouTube License, CC-BY