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

Videos

Textbook Question
Book Icon
Chapter 7.2, Problem 11E

Classify the quadratic forms in Exercises 9-18. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1.

11. 2 x 1 2 − 4 x 1 x 2 − x 2 2

Expert Solution & Answer
Check Mark

Want to see the full answer?

Check out a sample textbook solution
Blurred answer
Previous
Chapter 7.2, Problem 10E
Next
Chapter 7.2, Problem 12E

Chapter 7 Solutions

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

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 - a. An n n matrix that is orthogonally...Ch. 7.1 - a. There are symmetric matrices that are not...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. 35ECh. 7.1 - Let B be an n n symmetric matrix such that B2 =...Ch. 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 - Compute the quadratic form XTAX, when...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 - 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 - What is the largest possible value of the...Ch. 7.2 - What is the largest value of the quadratic form...Ch. 7.2 - In Exercises 21 and 22, matrices are n n and...Ch. 7.2 - In Exercises 21 and 22, matrices are n n and...Ch. 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. 26ECh. 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. 7.5 - 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 - Mark each statement True or False. Justify each...Ch. 7 - Prob. 2SECh. 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. 5SECh. 7 - Let A be an n n symmetric matrix. Use Exercise 5...Ch. 7 - Prove that an n n matrix A is positive definite...Ch. 7 - Use Exercise 7 to show that if A is positive...Ch. 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. 12SECh. 7 - Prob. 13SECh. 7 - Given any b in m, adapt Exercise 13 to show that...

Additional Math Textbook Solutions

Find more solutions based on key concepts
For each hour of class time, how many hours outside of class are recommended for studying and doing homework?

Elementary Algebra For College Students (10th Edition)

Graph each function. Identify the domain and range.

Glencoe Algebra 2 Student Edition C2014

A faucet can fill a sink in 5 minutes. It takes twice as long for the drain to empty the sink. How long will it...

Intermediate Algebra for College Students (7th Edition)

Silvia wants to mix a 40% apple juice drink with pure apple juice to make 2 L of a juice drink that is 80% appl...

Beginning and Intermediate Algebra

Factor and solve the quadratic equation: x25x6=0.

College Algebra

Exercise 117–120: For each function findand. 117.

College Algebra with Modeling & Visualization (6th Edition)

Knowledge Booster
Background pattern image
Algebra
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.
Recommended textbooks for you
Text book image
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Text book image
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
SEE MORE TEXTBOOKS
Interpreting Graphs of Quadratic Equations (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=BHgewRcuoRM;License: Standard YouTube License, CC-BY
Solve a Trig Equation in Quadratic Form Using the Quadratic Formula (Cosine, 4 Solutions); Author: Mathispower4u;https://www.youtube.com/watch?v=N6jw_i74AVQ;License: Standard YouTube License, CC-BY